Suppose , p = Z such that p is prime. If = 1 (mod p) 7281 (mod p) find the least positive integer e such that it must be true (for any possible value of a satisfying the congruences above) that x² = 1 (mod p). (Hint: consider taking products of 525, 728 or try small examples like x = 2, p = 7.) Type your answer... 2525 x

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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This Intro to Elementary Number Theory Homework problem is very difficult. 

 

Suppose , p = Z such that p is prime. If
= 1
(mod p)
7281 (mod p)
find the least positive integer e such that it must be true (for any possible value of a satisfying the congruences above) that
x² = 1
(mod p).
(Hint: consider taking products of 525, 728 or try small examples like x = 2, p = 7.)
Type your answer...
2525
x
Transcribed Image Text:Suppose , p = Z such that p is prime. If = 1 (mod p) 7281 (mod p) find the least positive integer e such that it must be true (for any possible value of a satisfying the congruences above) that x² = 1 (mod p). (Hint: consider taking products of 525, 728 or try small examples like x = 2, p = 7.) Type your answer... 2525 x
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