| 586 | Counting positive solutions | Easy | Lemma | Diophantine equations | |
| 587 | A difference of squares | Easy | Lemma | Diophantine equations | |
| 588 | A Pythagorean triple | Easy | Lemma | Diophantine equations | |
| 1358 | Linear Diophantine Equation 1 | Easy | Hall & Knight | Diophantine equationsLinear equations | |
| 1359 | Linear Diophantine Equation 2 | Easy | Hall & Knight | Diophantine equationsLinear equations | |
| 1360 | Linear Diophantine Equation 3 | Easy | Hall & Knight | Diophantine equationsLinear equations | |
| 1781 | Coupled Linear Indeterminate Equations | Easy | Hall & Knight | Linear Diophantine equationsSystems of equations | |
| 589 | Bézout coefficients | Medium | Lemma | Diophantine equations | |
| 590 | The largest impossible total | Medium | Classical | Diophantine equations | |
| 591 | Lattice points on a circle | Medium | Lemma | Diophantine equations | |
| 1361 | Linear Diophantine Equation 4 | Medium | Hall & Knight | Diophantine equationsLinear equations | |
| 1362 | Linear Diophantine Equation 5 | Medium | Hall & Knight | Diophantine equationsLinear equations | |
| 1363 | Linear Diophantine Equation 6 | Medium | Hall & Knight | Diophantine equationsLinear equations | |
| 1364 | Buying Horses and Cows | Medium | Hall & Knight | Diophantine equationsLinear equations | |
| 1365 | Paying Five Pounds in Shillings and Sixpences | Medium | Hall & Knight | Diophantine equationsCounting | |
| 1366 | Splitting Eighty-One | Medium | Hall & Knight | Diophantine equations | |
| 1367 | Paying with Guineas and Half-Crowns | Medium | Hall & Knight | Diophantine equationsCurrency | |
| 1369 | Discharging a Debt with Florins and Half-Crowns | Medium | Hall & Knight | Diophantine equationsCurrency | |
| 1772 | Linear Indeterminate Equation 1 | Medium | Hall & Knight | linear diophantine equationseuclidean algorithm | |
| 1773 | Linear Indeterminate Equation 2 | Medium | Hall & Knight | linear diophantine equationseuclidean algorithm | |
| 1774 | Linear Indeterminate Equation 3 | Medium | Hall & Knight | linear diophantine equationseuclidean algorithm | |
| 1775 | Paying an Amount in Coins | Medium | Hall & Knight | linear diophantine equationspositive integer solutions | |
| 1776 | Positive Solutions of Diophantine Equation | Medium | Hall & Knight | linear diophantine equationspositive integer solutions | |
| 1777 | Fractions with Given Denominators | Medium | Hall & Knight | linear diophantine equationsfractions | |
| 1778 | Fractional Difference Problem | Medium | Hall & Knight | Diophantine equationsProper fractions | |
| 1779 | System of Three Variables | Medium | Hall & Knight | Linear Diophantine equationsSystems of equations | |
| 1780 | System of Indeterminate Equations | Medium | Hall & Knight | Linear Diophantine equationsSystems of equations | |
| 1782 | Indeterminate Equations via Elimination | Medium | Hall & Knight | Linear Diophantine equationsSystems of equations | |
| 1783 | Three-variable linear Diophantine equation | Medium | Hall & Knight | Diophantine equationsPositive integers | |
| 1784 | Three-variable Diophantine equation | Medium | Hall & Knight | Diophantine equationsPositive integers | |
| 1788 | Harmonic progression with integer terms | Medium | Hall & Knight | Harmonic progressionDiophantine equations | |
| 1789 | Coincident Rod Divisions | Medium | Hall & Knight | Diophantine equationsLinear congruence | |
| 1790 | Tolling Bells | Medium | Hall & Knight | Diophantine equationsWord problems | |
| 1791 | Six Solutions Condition | Medium | Hall & Knight | Diophantine equationsInequalities | |
| 1792 | Five Solutions Condition | Medium | Hall & Knight | Diophantine equationsInequalities | |
| 1793 | Limits for Six Solutions | Medium | Hall & Knight | Diophantine equationsInequalities | |
| 1795 | Fifth convergent of a continued fraction | Medium | Hall & Knight | continued fractionsconvergents | |
| 1796 | Infinite continued fraction representation | Medium | Hall & Knight | continued fractionssurds | |
| 1800 | Product of two continued fractions | Medium | Hall & Knight | continued fractionsinfinite products | |
| 1801 | Periodic Continued Fractions Identity | Medium | Hall & Knight | continued fractionsinfinite fractions | |
| 1804 | Convergents of the Golden Ratio | Medium | Hall & Knight | continued fractionsFibonacci numbers | |
| 1805 | Difference of Two Continued Fractions | Medium | Hall & Knight | continued fractionsinfinite fractions | |
| 1794 | Extremal Values of Constant | Deep | Hall & Knight | Diophantine equationsProof | |
| 1797 | Scaling a continued fraction | Deep | Hall & Knight | continued fractionstransformations | |
| 1798 | Convergents of the square root of a sum | Deep | Hall & Knight | continued fractionsconvergents | |
| 1799 | Relation among periodic continued fractions | Deep | Hall & Knight | continued fractionsalgebraic identity | |
| 1802 | Sum of Convergents for Square Root | Deep | Hall & Knight | continued fractionsconvergents | |
| 1803 | Product of Infinite Continued Fractions | Deep | Hall & Knight | continued fractionsinfinite fractions | |
| 1806 | Convergents at Period Lengths | Deep | Hall & Knight | continued fractionsquadratic surds+1 | |
| 1807 | Periodicity of Surd Convergents | Deep | Hall & Knight | continued fractionsrecurring continued fractions+1 | |