期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2010
卷号：72
期号：01
页码：226--236
出版社：Indian Statistical Institute
摘要：We find by elementary methods the number of solutions of the equation
RX2+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.
关键词：Congruences, number of solutions, randomized algorithm,
Jacobi and Legendre symbols.
