Question

For a certain positive integer n, n^2 gives a remainder of 4 when divided by 5, and n^3 gives a remainder of 2 when divided by 5. What remainder does n give when divided by 5?

Answer 1

n^3 - n^ = -2 = 3 mod 5 => n^2(n-1) = 3 mod 5 8 = 3 mod 5, n^2 = 4 mod 5 => n-1 = 2 mod 5 so n = 3 mod 5