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
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
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 57E
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This Intro to Elementary Number Theory Homework problem is very difficult.
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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