Question

please do 7

7. (a) Let p be prime. Suppose a and b are integers such that ab = 0
(mod p). Show that either a = 0 or b = 0 (mod p).
(b) Show that if a, 6, n are integers with nlab and gcd(a, n) = 1, then
n|b.
8. Let p 2 3 be prime. Show that the only solutions to 1' = 1 (mod p)
are I = ±1 (mod p). (Hint: Apply Exercise 7(a) to (z+ 1)(1 - 1).)

Image Transcription

7. (a) Let p be prime. Suppose a and b are integers such that ab = 0 (mod p). Show that either a = 0 or b = 0 (mod p). (b) Show that if a, 6, n are integers with nlab and gcd(a, n) = 1, then n|b. 8. Let p 2 3 be prime. Show that the only solutions to 1' = 1 (mod p) are I = ±1 (mod p). (Hint: Apply Exercise 7(a) to (z+ 1)(1 - 1).)

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