Topic: Elementary Number Theory
Let x be an integer. let p be a prime. Suppose that x^2 == x mod p. Show that either x == 0 mod p, or x == 1 mod p
Note that we have
If x^2 ≡ x (mod p),
then x(x − 1) ≡ 0 (mod p).
Thus p | x(x − 1), so p | x or p | x − 1.
Hence the only solutions are x ≡ 0 (mod p) or x ≡ 1 (mod p).
Content will be erased after question is completed.
Enter the email address associated with your account, and we will email you a link to reset your password.
Forgot your password?