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Suppose , p € Z such that p is prime. If (mod p) = 1 (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 x 1 (mod p). 2580 = 1 783 (Hint: consider taking products of 580, x7 or try small examples like x = 2, p = 7.) Type your answer...

Suppose , p € Z such that p is prime. If (mod p) = 1 (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 x 1 (mod p). 2580 = 1 783 (Hint: consider taking products of 580, x7 or try small examples like x = 2, p = 7.) Type your answer...

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This Intro to Elementary Number Theory Homework problem is very difficult. 

 

 

 

Supposex, pe Z such that p is prime. If 580 X² = 1 (mod p) 7831 (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 580, 783 or try small examples like x = 2, p = 7.) Type your answer...
Transcribed Image Text:Supposex, pe Z such that p is prime. If 580 X² = 1 (mod p) 7831 (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 580, 783 or try small examples like x = 2, p = 7.) Type your answer...
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