Find the smallest positive integer r such that (Note that 3691 is prime.) Type your answer... x240r = 1 (mod 3,691).

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.7: Problem Solving: Consecutive Integers
Problem 14OE
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Intro to Elementary Number Theory Homework problems

 

Find the smallest positive integer r such that
(Note that 3691 is prime.)
Type your answer...
x240,
= 1 (mod 3,691).
Transcribed Image Text:Find the smallest positive integer r such that (Note that 3691 is prime.) Type your answer... x240, = 1 (mod 3,691).
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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