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：1
页码：226-236
DOI：10.1007/s13171-010-0010-9
语种：English
出版社：Indian Statistical Institute
摘要：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.
关键词：Congruences ; number of solutions ; randomized algorithm ; Jacobi and Legendre symbols
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