Abstract
We consider the regular continued fraction expansion of a rational number m/N, m ≥ 0, N ≥ 1, (m, N) = 1. Let s/t, (s, t) = 1, be the kth convergent of this expansion and p/q, (p, q) = 1, be the complete quotient belonging to s/t. We give some relations for Jacobi symbols, a typical example of which is [Formula: see text] for k, t, q, N odd, with a simple right-hand side depending on t, q, N (mod 4). As an application, we prove the periodicity of the Jacobi symbol [Formula: see text] for the convergents s/t of infinite purely periodic continued fractions.
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