#1800 · Number Theory · Diophantine equations

Product of two continued fractions

Prove that $(a + \frac{1}{b +} \frac{1}{a +} \frac{1}{b +} \frac{1}{a +} \dots) (\frac{1}{b +} \frac{1}{a +} \frac{1}{b +} \frac{1}{a +} \dots) = \frac{a}{b}$ .

~15 minProof · checked by AIcontinued fractionsinfinite products

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXVII. Recurring Continued Fractions, Examples XXVII.b, No. 12

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