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b) Let p≥ 3 be prime. Show that the only solutions to x² = 1 (mod p) are x = ±1 (mod p). Hint: Apply part a) to (x+1)(x−1)

b) Let p≥ 3 be prime. Show that the only solutions to x² = 1 (mod p) are x = ±1 (mod p). Hint: Apply part a) to (x+1)(x−1)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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b) Let p≥ 3 be prime. Show that the only solutions to x² =1 (mod p) are x = ±1 (mod p). Hint: Apply part a) to (x+1)(x-1)
Transcribed Image Text:b) Let p≥ 3 be prime. Show that the only solutions to x² =1 (mod p) are x = ±1 (mod p). Hint: Apply part a) to (x+1)(x-1)
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