Collection
Write a proof
Problems whose answer is an argument. Write it out, and Lemma checks whether every step holds.
Number theory
38 problems| # | Title | Difficulty | Source | Tags | |
|---|---|---|---|---|---|
| 2 | The primes never endPrime numbers | Medium | Lemma | ||
| 3 | A sum that's never wholeDivisibility | Deep | Lemma | ||
| 10 | A desert of primesPrime numbers | Medium | Lemma | ||
| 13 | Squares leave a traceDivisibility | Easy | Lemma | ||
| 1119 | Perfect square for large radicesDigits | Deep | Hall & Knight | ||
| 1120 | Square with invariant root digitsDigits | Deep | Hall & Knight | ||
| 1121 | Universal perfect cubeDigits | Deep | Hall & Knight | ||
| 1124 | Perfect‑cube in large basesDivisibility | Medium | Hall & Knight | ||
| 1125 | Divisibility by eight via last three digitsDivisibility | Easy | Hall & Knight | ||
| 1126 | Square of repeated digit in consecutive baseDivisibility | Medium | Hall & Knight | ||
| 1127 | Digit‑rearrangement differenceDivisibility | Medium | Hall & Knight | ||
| 1128 | Divisibility by $r+1$ for symmetric digitsDivisibility | Medium | Hall & Knight | ||
| 1129 | Digit‑sum differenceDivisibility | Medium | Hall & Knight | ||
| 1130 | Triple‑repeat divisibilityDivisibility | Medium | Hall & Knight | ||
| 1131 | Parity of digit sum in odd radixDivisibility | Medium | Hall & Knight | ||
| 1132 | Repeating‑digit divisorDivisibility | Deep | Hall & Knight | ||
| 1358 | Linear Diophantine Equation 1Diophantine equations | Easy | Hall & Knight | ||
| 1359 | Linear Diophantine Equation 2Diophantine equations | Easy | Hall & Knight | ||
| 1360 | Linear Diophantine Equation 3Diophantine equations | Easy | Hall & Knight | ||
| 1361 | Linear Diophantine Equation 4Diophantine equations | Medium | Hall & Knight | ||
| 1362 | Linear Diophantine Equation 5Diophantine equations | Medium | Hall & Knight | ||
| 1363 | Linear Diophantine Equation 6Diophantine equations | Medium | Hall & Knight | ||
| 1783 | Three-variable linear Diophantine equationDiophantine equations | Medium | Hall & Knight | ||
| 1784 | Three-variable Diophantine equationDiophantine equations | Medium | Hall & Knight | ||
| 1788 | Harmonic progression with integer termsDiophantine equations | Medium | Hall & Knight | ||
| 1794 | Extremal Values of ConstantDiophantine equations | Deep | Hall & Knight | ||
| 1796 | Infinite continued fraction representationDiophantine equations | Medium | Hall & Knight | ||
| 1797 | Scaling a continued fractionDiophantine equations | Deep | Hall & Knight | ||
| 1798 | Convergents of the square root of a sumDiophantine equations | Deep | Hall & Knight | ||
| 1799 | Relation among periodic continued fractionsDiophantine equations | Deep | Hall & Knight | ||
| 1800 | Product of two continued fractionsDiophantine equations | Medium | Hall & Knight | ||
| 1801 | Periodic Continued Fractions IdentityDiophantine equations | Medium | Hall & Knight | ||
| 1802 | Sum of Convergents for Square RootDiophantine equations | Deep | Hall & Knight | ||
| 1803 | Product of Infinite Continued FractionsDiophantine equations | Deep | Hall & Knight | ||
| 1804 | Convergents of the Golden RatioDiophantine equations | Medium | Hall & Knight | ||
| 1805 | Difference of Two Continued FractionsDiophantine equations | Medium | Hall & Knight | ||
| 1806 | Convergents at Period LengthsDiophantine equations | Deep | Hall & Knight | ||
| 1807 | Periodicity of Surd ConvergentsDiophantine equations | Deep | Hall & Knight |
Algebra & inequalities
267 problems| # | Title | Difficulty | Source | Tags | |
|---|---|---|---|---|---|
| 6 | The mean of twoInequalities | Easy | Lemma | ||
| 12 | Integer echoesRecurrences | Medium | Lemma | ||
| 47 | Three fractions, at least threeInequalities | Deep | Lemma | ||
| 50 | A dot product can't be too bigInequalities | Deep | Lemma | ||
| 223 | Groups of prime orderSubgroups & cosets | Easy | Lemma | ||
| 545 | Intersections are subgroupsSubgroups & cosets | Easy | Lemma | ||
| 813 | Arithmetic means between fractionsSequences & series | Medium | Hall & Knight | ||
| 814 | Arithmetic means between mixed numbersSequences & series | Medium | Hall & Knight | ||
| 815 | Arithmetic means with variable termSequences & series | Medium | Hall & Knight | ||
| 816 | Arithmetic means with quadratic endpointsSequences & series | Deep | Hall & Knight | ||
| 837 | Relation among three termsSequences & series | Medium | Hall & Knight | ||
| 844 | Relation of terms from sum ratiosSequences & series | Deep | Hall & Knight | ||
| 932 | Proving an Algebraic Ratio IdentityLinear equations | Medium | Hall & Knight | ||
| 933 | Continued Proportion IdentityLinear equations | Medium | Hall & Knight | ||
| 934 | Symmetric Ratio RelationLinear equations | Medium | Hall & Knight | ||
| 935 | Cyclic Sum Ratio IdentityLinear equations | Deep | Hall & Knight | ||
| 936 | Fractional Sum with CubesLinear equations | Medium | Hall & Knight | ||
| 937 | Reciprocal proportionalityLinear equations | Medium | Hall & Knight | ||
| 938 | Equality case of Cauchy–SchwarzLinear equations | Medium | Hall & Knight | ||
| 939 | Cyclic proportionalityLinear equations | Medium | Hall & Knight | ||
| 940 | Eliminant of a symmetric systemLinear equations | Deep | Hall & Knight | ||
| 942 | Quadratic ratios from cyclic definitionsLinear equations | Deep | Hall & Knight | ||
| 943 | Relation among three variablesLinear equations | Medium | Hall & Knight | ||
| 948 | Relations among three fractional expressionsLinear equations | Deep | Hall & Knight | ||
| 950 | Proportionality from cyclic relationsFunctional equations | Deep | Hall & Knight | ||
| 953 | Proportion Identity Proof OneSequences & series | Medium | Hall & Knight | ||
| 954 | Proportion Identity Proof TwoSequences & series | Medium | Hall & Knight | ||
| 955 | Proportion Identity Proof ThreeSequences & series | Medium | Hall & Knight | ||
| 956 | Proportion radical identityLinear equations | Medium | Hall & Knight | ||
| 957 | Continued proportion identity ILinear equations | Medium | Hall & Knight | ||
| 958 | Continued proportion identity IILinear equations | Medium | Hall & Knight | ||
| 959 | Continued proportion identity IIILinear equations | Medium | Hall & Knight | ||
| 960 | Mean proportional algebraic relationLinear equations | Medium | Hall & Knight | ||
| 961 | Product proportion identityLinear equations | Medium | Hall & Knight | ||
| 965 | Prove proportion identityLinear equations | Deep | Hall & Knight | ||
| 966 | Continued proportion identityLinear equations | Deep | Hall & Knight | ||
| 971 | Inequality for four continued proportionalsInequalities | Deep | Hall & Knight | ||
| 980 | Combination of variationsFunctions | Medium | Hall & Knight | ||
| 981 | Derived inverse variationFunctions | Medium | Hall & Knight | ||
| 983 | Variation of Quadratic SumsFunctional equations | Medium | Hall & Knight | ||
| 988 | Prove variation of AFunctions | Medium | Hall & Knight | ||
| 993 | Diamond and Gold Ring ValuesSequences & series | Medium | Hall & Knight | ||
| 1007 | Inserting Geometric MeansSequences & series | Medium | Hall & Knight | ||
| 1020 | Relation between geometric series sumsSequences & series | Medium | Hall & Knight | ||
| 1021 | Exponential relation of GP termsSequences & series | Medium | Hall & Knight | ||
| 1029 | Compare terms of two progressionsSequences & series | Medium | Hall & Knight | ||
| 1030 | Sum of geometric series equalitySequences & series | Medium | Hall & Knight | ||
| 1038 | Relation among four consecutive G.P. termsSequences & series | Medium | Hall & Knight | ||
| 1039 | Arithmetic and geometric mean conditionSequences & series | Medium | Hall & Knight | ||
| 1043 | Sum of infinite geometric seriesSequences & series | Medium | Hall & Knight | ||
| 1044 | Limit of a geometric termSequences & series | Deep | Hall & Knight | ||
| 1048 | Ratio from meansSequences & series | Deep | Hall & Knight | ||
| 1049 | Proportion in harmonic progressionSequences & series | Medium | Hall & Knight | ||
| 1050 | Harmonical Progression PropertySequences & series | Medium | Hall & Knight | ||
| 1051 | Terms of a Harmonical ProgressionSequences & series | Medium | Hall & Knight | ||
| 1052 | Harmonic Mean RelationSequences & series | Easy | Hall & Knight | ||
| 1059 | Ratio of difference to first termSequences & series | Deep | Hall & Knight | ||
| 1060 | Relation of first term to differenceSequences & series | Deep | Hall & Knight | ||
| 1061 | Nth term from quadratic sumSequences & series | Medium | Hall & Knight | ||
| 1063 | Means ratio identitySequences & series | Medium | Hall & Knight | ||
| 1064 | Bounds for harmonic meansSequences & series | Deep | Hall & Knight | ||
| 1077 | Shot count in square vs triangular pileSequences & series | Medium | Hall & Knight | ||
| 1198 | Cube roots of unity identityRoots of unity | Easy | Hall & Knight | ||
| 1199 | Product involving cube rootsLinear equations | Medium | Hall & Knight | ||
| 1200 | Power of binomials with omegaLinear equations | Medium | Hall & Knight | ||
| 1201 | Product of $2n$ factors with omegaLinear equations | Deep | Hall & Knight | ||
| 1202 | Sum of cubes factorizationLinear equations | Medium | Hall & Knight | ||
| 1203 | Symmetric Product of Linear FormsPolynomials | Deep | Hall & Knight | ||
| 1226 | Real roots of quadratic equationQuadratics | Easy | Hall & Knight | ||
| 1230 | Signs of quadratic rootsQuadratics | Medium | Hall & Knight | ||
| 1232 | Bounds of a rational fractionQuadratics | Medium | Hall & Knight | ||
| 1233 | Bounds of a symmetric fractionQuadratics | Medium | Hall & Knight | ||
| 1234 | Excluded values of a fractionQuadratics | Medium | Hall & Knight | ||
| 1236 | Ratio of roots identityQuadratics | Medium | Hall & Knight | ||
| 1237 | Range of a rational expressionQuadratics | Medium | Hall & Knight | ||
| 1238 | Difference of roots invarianceQuadratics | Medium | Hall & Knight | ||
| 1239 | Parameter bounds for real valuesQuadratics | Medium | Hall & Knight | ||
| 1241 | Excluded values of a rational expressionQuadratics | Medium | Hall & Knight | ||
| 1242 | Condition for Impossible RootsQuadratics | Medium | Hall & Knight | ||
| 1243 | Range of a Rational ExpressionQuadratics | Deep | Hall & Knight | ||
| 1246 | Real linear factorsQuadratics | Medium | Hall & Knight | ||
| 1247 | Common root of two quadraticsQuadratics | Medium | Hall & Knight | ||
| 1248 | Parameter for linear factorsQuadratics | Deep | Hall & Knight | ||
| 1249 | Real values in a quadratic relationQuadratics | Medium | Hall & Knight | ||
| 1250 | Bounds for variables in a quadratic relationQuadratics | Medium | Hall & Knight | ||
| 1373 | Sum of odd integersSequences & series | Easy | Hall & Knight | ||
| 1374 | Sum of squaresSequences & series | Easy | Hall & Knight | ||
| 1375 | Sum of powers of twoSequences & series | Easy | Hall & Knight | ||
| 1376 | Telescoping series sumSequences & series | Easy | Hall & Knight | ||
| 1377 | Divisibility of difference of powersPolynomials | Medium | Hall & Knight | ||
| 1410 | Coefficient of x to the pSequences & series | Medium | Hall & Knight | ||
| 1417 | Middle terms of binomial expansionsPolynomials | Medium | Hall & Knight | ||
| 1418 | Sum of odd and even termsPolynomials | Medium | Hall & Knight | ||
| 1426 | Middle Term of BinomialSequences & series | Medium | Hall & Knight | ||
| 1427 | Sum of Weighted Coefficients ISequences & series | Easy | Hall & Knight | ||
| 1428 | Sum of Weighted Coefficients IISequences & series | Medium | Hall & Knight | ||
| 1429 | Binomial coefficient sum relationLinear equations | Medium | Hall & Knight | ||
| 1430 | Product of adjacent binomial coefficientsLinear equations | Deep | Hall & Knight | ||
| 1431 | Weighted sum of binomial coefficientsLinear equations | Medium | Hall & Knight | ||
| 1432 | Sum of squared binomial coefficientsLinear equations | Medium | Hall & Knight | ||
| 1433 | Sum of products of binomial coefficientsLinear equations | Deep | Hall & Knight | ||
| 1479 | Coefficient in Negative Power ExpansionSequences & series | Medium | Hall & Knight | ||
| 1480 | Transformed Binomial ExpansionSequences & series | Deep | Hall & Knight | ||
| 1483 | Binomial coefficient relationSequences & series | Medium | Hall & Knight | ||
| 1488 | Prove an infinite series identitySequences & series | Medium | Hall & Knight | ||
| 1489 | Prove a root series identitySequences & series | Medium | Hall & Knight | ||
| 1490 | Binomial Series Identity TransformationSequences & series | Medium | Hall & Knight | ||
| 1491 | Equivalence of Binomial SeriesSequences & series | Medium | Hall & Knight | ||
| 1492 | Approximate Expansion of FunctionSequences & series | Medium | Hall & Knight | ||
| 1493 | Parity of Surd Power Integer PartSequences & series | Medium | Hall & Knight | ||
| 1494 | Parity of Another Surd PowerSequences & series | Medium | Hall & Knight | ||
| 1496 | Middle Term Coefficient IdentityLinear equations | Deep | Hall & Knight | ||
| 1497 | Expansion Form of Cubic PowerLinear equations | Deep | Hall & Knight | ||
| 1498 | Coefficient Periodic PatternLinear equations | Medium | Hall & Knight | ||
| 1499 | Factorial Series Identity for Even nLinear equations | Medium | Hall & Knight | ||
| 1501 | Surd Power Fractional Part PropertyExponentials & logarithms | Medium | Hall & Knight | ||
| 1502 | Alternating Harmonic Series of Binomial CoefficientsSequences & series | Medium | Hall & Knight | ||
| 1503 | Quadratic form ratiosLinear equations | Deep | Hall & Knight | ||
| 1504 | Product identity for cofactorsLinear equations | Deep | Hall & Knight | ||
| 1514 | Symmetric combinations of variables with omega (part 1)Linear equations | Medium | Hall & Knight | ||
| 1515 | Symmetric combinations of variables with omega (part 2)Linear equations | Medium | Hall & Knight | ||
| 1516 | Symmetric combinations of variables with omega (part 3)Linear equations | Medium | Hall & Knight | ||
| 1517 | Real roots of quadratic equation 1Quadratics | Medium | Hall & Knight | ||
| 1518 | Real roots of quadratic equation 2Quadratics | Medium | Hall & Knight | ||
| 1519 | Rational roots of quadratic equation 1Quadratics | Medium | Hall & Knight | ||
| 1520 | Rational roots of quadratic equation 2Quadratics | Deep | Hall & Knight | ||
| 1531 | Alternating Binomial Coefficient IdentityLinear equations | Medium | Hall & Knight | ||
| 1532 | Weighted Alternating Binomial SumLinear equations | Medium | Hall & Knight | ||
| 1533 | Sum of Squares of Alternating CoefficientsLinear equations | Deep | Hall & Knight | ||
| 1534 | Sum of Natural Numbers Series ExpansionSequences & series | Medium | Hall & Knight | ||
| 1535 | Sum Identity with Triangular NumbersSequences & series | Deep | Hall & Knight | ||
| 1536 | Sum of Products of q CoefficientsSequences & series | Deep | Hall & Knight | ||
| 1537 | Alternating Sum of q ProductsSequences & series | Deep | Hall & Knight | ||
| 1556 | Thirds of Trinomial Expansion CoefficientsPolynomials | Deep | Hall & Knight | ||
| 1564 | Logarithmic identity proofExponentials & logarithms | Medium | Hall & Knight | ||
| 1566 | Prove a logarithmic relationExponentials & logarithms | Medium | Hall & Knight | ||
| 1571 | Logarithmic systemExponentials & logarithms | Easy | Hall & Knight | ||
| 1572 | Prove an exponential relationExponentials & logarithms | Medium | Hall & Knight | ||
| 1589 | Inequality with large powersExponentials & logarithms | Medium | Hall & Knight | ||
| 1625 | Discount as harmonic meanExponentials & logarithms | Medium | Hall & Knight | ||
| 1626 | Century of Compound InterestExponentials & logarithms | Medium | Hall & Knight | ||
| 1640 | Depleting CapitalSequences & series | Deep | Hall & Knight | ||
| 1642 | Annuity Purchase RelationsSequences & series | Deep | Hall & Knight | ||
| 1644 | Positive inequality productInequalities | Easy | Hall & Knight | ||
| 1645 | Symmetric triple sum productInequalities | Easy | Hall & Knight | ||
| 1646 | Quantity and reciprocal sumInequalities | Easy | Hall & Knight | ||
| 1647 | Cauchy-Schwarz case for two variablesInequalities | Easy | Hall & Knight | ||
| 1648 | Cauchy-Schwarz case for three variablesInequalities | Easy | Hall & Knight | ||
| 1649 | Exponential and logarithmic inequalitiesInequalities | Medium | Hall & Knight | ||
| 1650 | Algebraic Inequality ProductInequalities | Medium | Hall & Knight | ||
| 1652 | Symmetric InequalityInequalities | Easy | Hall & Knight | ||
| 1653 | Sum of Products InequalityInequalities | Medium | Hall & Knight | ||
| 1654 | Squares InequalityInequalities | Medium | Hall & Knight | ||
| 1655 | Inequality with CubicsInequalities | Medium | Hall & Knight | ||
| 1657 | Cube of Sum InequalityInequalities | Easy | Hall & Knight | ||
| 1658 | Power and Odd Product InequalityInequalities | Medium | Hall & Knight | ||
| 1659 | Inequality with powers and rootsInequalities | Deep | Hall & Knight | ||
| 1660 | Factorial inequalityInequalities | Deep | Hall & Knight | ||
| 1663 | Fourth Power InequalityInequalities | Medium | Hall & Knight | ||
| 1664 | Sum of Cubes InequalityInequalities | Medium | Hall & Knight | ||
| 1665 | Sum of Even PowersInequalities | Deep | Hall & Knight | ||
| 1666 | Growth of Exponential ExpressionsInequalities | Deep | Hall & Knight | ||
| 1667 | Descending Variables InequalityInequalities | Deep | Hall & Knight | ||
| 1668 | Weighted Power InequalityInequalities | Medium | Hall & Knight | ||
| 1669 | Logarithmic inequality for powersInequalities | Medium | Hall & Knight | ||
| 1670 | Fractional power inequalityInequalities | Medium | Hall & Knight | ||
| 1671 | Harmonic progression power inequalityInequalities | Medium | Hall & Knight | ||
| 1672 | Logarithm boundsInequalities | Easy | Hall & Knight | ||
| 1673 | Cauchy-Schwarz Inequality ApplicationInequalities | Medium | Hall & Knight | ||
| 1674 | Positivity of Symmetric ExpressionsInequalities | Medium | Hall & Knight | ||
| 1675 | Power Inequality for ExponentsInequalities | Medium | Hall & Knight | ||
| 1676 | Weighted Arithmetic Mean InequalityInequalities | Medium | Hall & Knight | ||
| 1677 | Factorial Product InequalityInequalities | Medium | Hall & Knight | ||
| 1678 | Minimum product of factorialsInequalities | Deep | Hall & Knight | ||
| 1723 | Conditions for a Bivariate Quadratic SquarePolynomials | Medium | Hall & Knight | ||
| 1724 | Cubic Divisible by Quadratic Sum of SquaresPolynomials | Medium | Hall & Knight | ||
| 1725 | Quintic Divisible by a Squared Linear FactorPolynomials | Medium | Hall & Knight | ||
| 1727 | Sum of Products of PowersPolynomials | Deep | Hall & Knight | ||
| 1734 | Series Expansion of Implicit FunctionSequences & series | Medium | Hall & Knight | ||
| 1736 | Infinite Product CoefficientSequences & series | Deep | Hall & Knight | ||
| 1757 | Homogeneous products of three variablesPolynomials | Deep | Hall & Knight | ||
| 1767 | Scales of relation for powersSequences & series | Medium | Hall & Knight | ||
| 1768 | Sum of recurring series from infinitySequences & series | Medium | Hall & Knight | ||
| 1770 | Scales of recurring series productSequences & series | Deep | Hall & Knight | ||
| 1771 | Scale of summed recurring seriesSequences & series | Deep | Hall & Knight | ||
| 1824 | Sum of Multinomial CoefficientsPolynomials | Medium | Hall & Knight | ||
| 1825 | Weighted Sum of CoefficientsPolynomials | Deep | Hall & Knight | ||
| 1859 | Position of first significant figure for \bar{2}.7781513Exponentials & logarithms | Easy | Hall & Knight | ||
| 1860 | Position of first significant figure for .6910815Exponentials & logarithms | Easy | Hall & Knight | ||
| 1861 | Position of first significant figure for \bar{5}.4871384Exponentials & logarithms | Easy | Hall & Knight | ||
| 1866 | Factorial and Power InequalityInequalities | Medium | Hall & Knight | ||
| 1867 | Product and Power InequalityInequalities | Medium | Hall & Knight | ||
| 1868 | Cubic variables inequality first partInequalities | Medium | Hall & Knight | ||
| 1869 | Cubic variables inequality second partInequalities | Medium | Hall & Knight | ||
| 1872 | Minimum sum of reciprocalsInequalities | Easy | Hall & Knight | ||
| 1873 | Product inequality from sum constraintInequalities | Medium | Hall & Knight | ||
| 1874 | Triangle Side Quadratic Non-negativityInequalities | Deep | Hall & Knight | ||
| 1875 | Triangle Side Expression Sign ConstraintInequalities | Deep | Hall & Knight | ||
| 1885 | Lagrange Interpolation Identity QuadraticPolynomials | Medium | Hall & Knight | ||
| 1886 | Lagrange Interpolation Identity CubicPolynomials | Medium | Hall & Knight | ||
| 1887 | Finite Series Identity OneSequences & series | Medium | Hall & Knight | ||
| 1888 | Finite Series Identity TwoSequences & series | Medium | Hall & Knight | ||
| 1889 | Finite Series Identity ThreeSequences & series | Medium | Hall & Knight | ||
| 1890 | Finite Series Identity FourSequences & series | Medium | Hall & Knight | ||
| 1898 | Symmetric functions of powersPolynomials | Deep | Hall & Knight | ||
| 1899 | An inequality with positive numbersInequalities | Deep | Hall & Knight | ||
| 1900 | Sum of homogeneous productsSequences & series | Deep | Hall & Knight | ||
| 1901 | Sum of binomial series coefficientsSequences & series | Deep | Hall & Knight | ||
| 1902 | Symmetric Equal ProductsSystems | Deep | Hall & Knight | ||
| 1903 | Real Triads of SolutionsSystems | Deep | Hall & Knight | ||
| 1904 | Algebraic Identity VerificationPolynomials | Deep | Hall & Knight | ||
| 1907 | Identity with fourth powersPolynomials | Deep | Hall & Knight | ||
| 99617 | Polynomials · Exercise 1Polynomials | Easy | OpenStax | ||
| 100734 | Domain and Range · Exercise 11Functions | Easy | OpenStax | ||
| 100857 | Composition of Functions · Exercise 8Functions | Easy | OpenStax | ||
| 101288 | Linear Functions · Exercise 17Graphs | Easy | OpenStax | ||
| 101591 | Quadratic Functions · Exercise 8Quadratics | Easy | OpenStax | ||
| 101763 | Using the Intermediate Value TheoremPolynomials | Easy | OpenStax | ||
| 101764 | Graphs of Polynomial Functions · Try It 3Polynomials | Easy | OpenStax | ||
| 102140 | Verifying Inverse FunctionsPolynomials | Easy | OpenStax | ||
| 102141 | Inverses and Radical Functions · Try It 1Polynomials | Easy | OpenStax | ||
| 102153 | Inverses and Radical Functions · Exercise 11Polynomials | Easy | OpenStax | ||
| 102395 | Exponential Functions · Exercise 10Exponentials & logarithms | Easy | OpenStax | ||
| 104992 | Systems of Linear Equations: Two Variables · Exercise 5Systems | Easy | OpenStax | ||
| 105083 | Systems of Linear Equations: Three Variables · Exercise 4Systems | Easy | OpenStax | ||
| 105085 | Systems of Linear Equations: Three Variables · Exercise 6Systems | Easy | OpenStax | ||
| 105164 | Systems of Nonlinear Equations and Inequalities: Two Variables · Exercise 4Systems | Easy | OpenStax | ||
| 105166 | Systems of Nonlinear Equations and Inequalities: Two Variables · Exercise 6Systems | Easy | OpenStax | ||
| 105233 | Partial Fractions · Exercise 2Partial fractions | Easy | OpenStax | ||
| 105313 | Matrices and Matrix Operations · Exercise 7Matrices | Easy | OpenStax | ||
| 105317 | Matrices and Matrix Operations · Exercise 11Matrices | Easy | OpenStax | ||
| 105392 | Solving Systems with Gaussian Elimination · Exercise 3Matrices | Easy | OpenStax | ||
| 105396 | Solving Systems with Gaussian Elimination · Exercise 7Matrices | Easy | OpenStax | ||
| 105458 | Showing That the Identity Matrix Acts as a 1Matrices | Easy | OpenStax | ||
| 105459 | Showing That Matrix A Is the Multiplicative Inverse of Matrix BMatrices | Easy | OpenStax | ||
| 105460 | Solving Systems with Inverses · Try It 1Matrices | Easy | OpenStax | ||
| 105547 | Solving Systems with Cramer's Rule · Exercise 3Determinants | Easy | OpenStax | ||
| 127986 | Rational Numbers · Example 21Ratio, proportion & variation | Easy | OpenStax | ||
| 128031 | Scientific Notation · Example 1Exponents & roots | Easy | OpenStax | ||
| 126434 | Finding Composite and Inverse Functions · Try It 9Exponentials & logarithms | Easy | OpenStax | ||
| 126435 | Finding Composite and Inverse Functions · Try It 10Exponentials & logarithms | Easy | OpenStax | ||
| 134676 | …Linear systems | Easy | Strang | ||
| 134677 | …Linear systems | Easy | Strang | ||
| 134678 | …Linear systems | Easy | Strang | ||
| 134679 | …Linear systems | Easy | Strang | ||
| 134680 | …Linear systems | Easy | Strang | ||
| 134681 | …Linear systems | Easy | Strang | ||
| 134682 | …Linear systems | Easy | Strang | ||
| 134683 | …Linear systems | Easy | Strang | ||
| 100258 | Complex Numbers · Exercise 64Arithmetic of ℂ | Medium | OpenStax | ||
| 101218 | Inverse Functions · Exercise 133Functions | Medium | OpenStax | ||
| 105477 | Solving Systems with Inverses · Exercise 10Matrices | Medium | OpenStax | ||
| 105479 | Solving Systems with Inverses · Exercise 12Matrices | Medium | OpenStax | ||
| 105481 | Solving Systems with Inverses · Exercise 14Matrices | Medium | OpenStax | ||
| 126877 | Solve Exponential and Logarithmic Equations · Review Exercise 80Exponentials & logarithms | Medium | OpenStax | ||
| 109232 | Add Integers · Exercise 63Integers | Medium | OpenStax | ||
| 109359 | Subtract Integers · Exercise 83Integers | Medium | OpenStax | ||
| 109559 | Solve Equations Using Integers; The Division Property of Equality · Exercise 67Linear equations | Medium | OpenStax | ||
| 107792 | Derivatives · Review Exercise 108Expressions | Medium | OpenStax | ||
| 107808 | Derivatives · Exercise 127Expressions | Medium | OpenStax | ||
| 134367 | Prove that the four fourth roots of … multiply to givePolar form | Medium | Strang | ||
| 134703 | Show that the determinant of … is …:Linear systems | Medium | Strang | ||
| 100093 | Linear Equations in One Variable · Exercise 70Inequalities | Deep | OpenStax | ||
| 102778 | Logarithmic Properties · Exercise 52Exponentials & logarithms | Deep | OpenStax | ||
| 102948 | Exponential and Logarithmic Models · Exercise 31Exponentials & logarithms | Deep | OpenStax | ||
| 134379 | Show that … and find a similar formula forPolar form | Deep | Strang | ||
| 134383 | Show that … andPolar form | Deep | Strang |