Abstract
We find by elementary methods the number of solutions of the equation RX 2 + SY 2 ≡ 1 (mod N), where N is an RSA composite and R, S are given integers coprime to N. When S (or R) is a square modulo N and its square root is known, our approach gives a very simple randomized algorithm for finding a solution. We also find the number of solutions in terms of Legendre and Jacobi symbols.
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