On the number of solutions of the equation Rx2 + Sy2 = 1 (mod N)

被引：0
|
作者：
Rana Barua
Mahabir P. Jhanwar
机构：
[1] Indian Statistical Institute,Stat
[2] Indian Statistical Institute,Math Unit
来源：
Sankhya A | 2010年 / 72卷 / 1期
关键词：
Congruences; number of solutions; randomized algorithm; Jacobi and Legendre symbols; Primary 11D79, 11D45; Secondary 11T71;
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学科分类号：
摘要：
We find by elementary methods the number of solutions of the equation RX2 + SY2 ≡ 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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页码：226 / 236
页数：10
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