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Identify if the given statement is true or false: I. If a is an integer, the (a^2 is congruent to 0 mod 4) II. If a is congruent to b (mod m), then a^k is congruent to bk (mod m) for every integers a, b, k and m III. When 314^162 is divided b

Identify if the given statement is true or false: I. If a is an integer, the (a^2 is congruent to 0 mod 4) II. If a is congruent to b (mod m), then a^k is congruent to bk (mod m) for every integers a, b, k and m III. When 314^162 is divided b

Elements Of Modern Algebra
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 30E: 30. Prove that any positive integer is congruent to its units digit modulo .
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Identify if the given statement is true or false: I. If a is an integer, the (a^2 is congruent to 0 mod 4) II. If a is congruent to b (mod m), then a^k is congruent to bk (mod m) for every integers a, b, k and m III. When 314^162 is divided by 162, then remainder is 3. IV. If (a, b) = d and d | m, then (ax is congruent to b mod m) has exactly d incongruent solutions modulo m for any integers a, b, and m with m > 0.
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