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(b) Wilson's Theorem: Let p be prime. Then (p-1)!= -1(mod p). Hint: Verify for p = 2 and p = 3 directly. Let p > 3 and note p-3 is even. Each of numbers in the set {2,3,...,p-2} has an inverse distinct from itself in the set. Take the product of the members in the set.

(b) Wilson's Theorem: Let p be prime. Then (p-1)!= -1(mod p). Hint: Verify for p = 2 and p = 3 directly. Let p > 3 and note p-3 is even. Each of numbers in the set {2,3,...,p-2} has an inverse distinct from itself in the set. Take the product of the members in the set.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 38E
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I need help with part b.

Prove the following lemma and Wilson's Theorem. (a) Lemma: If p is prime and a² = 1(mod p), then a = 1(mod p) or a = -1(mod p). (b) Wilson's Theorem: Let p be prime. Then (p-1)!= -1(mod p). Hint: Verify for p = 2 and p = 3 directly. Let p > 3 and note p-3 is even. Each of numbers in the set {2,3,...,p-2} has an inverse distinct from itself in the set. Take the product of the members in the set.
Transcribed Image Text:Prove the following lemma and Wilson's Theorem. (a) Lemma: If p is prime and a² = 1(mod p), then a = 1(mod p) or a = -1(mod p). (b) Wilson's Theorem: Let p be prime. Then (p-1)!= -1(mod p). Hint: Verify for p = 2 and p = 3 directly. Let p > 3 and note p-3 is even. Each of numbers in the set {2,3,...,p-2} has an inverse distinct from itself in the set. Take the product of the members in the set.
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