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Find the smallest positive integer r such that (Note that 2113 is prime.) Type your answer... 224r 1 (mod 2,113).

Find the smallest positive integer r such that (Note that 2113 is prime.) Type your answer... 224r 1 (mod 2,113).

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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Need help with these two Intro to Elementary Number Theory Homework problems.

 

Find the smallest positive integer r such that (Note that 2113 is prime.) Type your answer... x 224r = 1 (mod 2, 113).
Transcribed Image Text:Find the smallest positive integer r such that (Note that 2113 is prime.) Type your answer... x 224r = 1 (mod 2, 113).
Supposex, p € Z such that p is prime. If x540 1 (mod p) x740 = 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). (Hint: consider taking products of 540, 740 or try small examples like x = 2, p = 7.) Type your answer...
Transcribed Image Text:Supposex, p € Z such that p is prime. If x540 1 (mod p) x740 = 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). (Hint: consider taking products of 540, 740 or try small examples like x = 2, p = 7.) Type your answer...
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