i need Question 2 (1) (a) Show that the relation a = b mod n if n | a - b is an equivalence relation(b) Show that the binary operations + is well-defined modulo n.(2) If a = b mod n and a = b mod m and ged(m, n) = 1, then a = b mod mn.(3) Show that for any n E N,n(n + 1)(2n + 1)k=1(4) Let p be a prime number. Then r2 = 1 mod p has exactly two solutionsmodulo p.

Name: i need Question 2 (1) (a) Show that the relation a = b mod n if n | a
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Description: i need Question 2 (1) (a) Show that the relation a = b mod n if n | a - b is an equivalence relation(b) Show that the binary operations + is well-defined modulo n.(2) If a = b mod n and a = b mod m and ged(m, n) = 1, then a = b mod mn.(3) Show that

The greatest common divisor of two or more integers, which are not all zero, is the largest positive…

Answered: (2) If a = b modn and a = b mod m and…

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(2) If a = b modn and a = b mod m and ged(m, n): 1. then a =b mod mn.

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 58E: a. Prove that 10n(1)n(mod11) for every positive integer n. b. Prove that a positive integer z is...

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