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Show that (a + p)P = a (mod p2), where p is prime, and that, more generally, a = b (mod p) ⇒a= b (mod p²).

Show that (a + p)P = a (mod p2), where p is prime, and that, more generally, a = b (mod p) ⇒a= b (mod p²).

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 37E
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Show that (a + p)P = aP (mod p2), where p is prime, and that, more generally, a = b (mod p) ⇒a= b (mod p²).
Transcribed Image Text:Show that (a + p)P = aP (mod p2), where p is prime, and that, more generally, a = b (mod p) ⇒a= b (mod p²).
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