#1803 · Number Theory · Diophantine equations

Product of Infinite Continued Fractions

Show that $\frac{1}{a + \frac{1}{b + \frac{1}{c + \dots}}} c + \frac{1}{b + \frac{1}{a + \frac{1}{c + \dots}}} = \frac{1 + b c}{1 + ab}$ .

~25 minProof · checked by AIcontinued fractionsinfinite fractions

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXVII. Recurring Continued Fractions, Examples XXVII.b, No. 15

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