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a.) Prove that if p is prime and p = 1 (mod 4), then ((P₂1)!)² = -1 (mod p) b.) Use part (a.) to find an integer that satisfies the congruence x²= -1 (mod 17)

a.) Prove that if p is prime and p = 1 (mod 4), then ((P₂1)!)² = -1 (mod p) b.) Use part (a.) to find an integer that satisfies the congruence x²= -1 (mod 17)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 23E
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Both part (a.) and (b.) please. 

a.) Prove that if p is prime and p = 1 (mod 4), then ((P₂1)!)² = -1 (mod p) b.) Use part (a.) to find an integer that satisfies the congruence x²= -1 (mod 17)
Transcribed Image Text:a.) Prove that if p is prime and p = 1 (mod 4), then ((P₂1)!)² = -1 (mod p) b.) Use part (a.) to find an integer that satisfies the congruence x²= -1 (mod 17)
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