#1805 · Number Theory · Diophantine equations

Difference of Two Continued Fractions

Prove that the difference of the infinite continued fractions $\frac{1}{a + \frac{1}{b + \frac{1}{c + \dots}}}$ and $\frac{1}{b + \frac{1}{a + \frac{1}{c + \dots}}}$ is equal to $\frac{a - b}{1 + ab}$ .

~15 minProof · checked by AIcontinued fractionsinfinite fractions

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXVII. Recurring Continued Fractions, Examples XXVII.b, No. 17

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