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Let p be an odd prime, and let a € Z represent a primitive root mod p. Show that a + tp represents a primitive root mod p² if and only if t does not satisfy pt = a³ — a (mod p²).

Let p be an odd prime, and let a € Z represent a primitive root mod p. Show that a + tp represents a primitive root mod p² if and only if t does not satisfy pt = a³ — a (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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Let p be an odd prime, and let a € Z represent a primitive root mod p. Show that a + tp represents a primitive root mod p² if and only if t does not satisfy pt = a³ — a (mod p²).
Transcribed Image Text:Let p be an odd prime, and let a € Z represent a primitive root mod p. Show that a + tp represents a primitive root mod p² if and only if t does not satisfy pt = a³ — a (mod p²).
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