Prove that n is a prime number greater than 5 then n^4 has final digit 1

Last digit of n determines last digit of n^4. All even numbers divide by 2, so are not prime. Any number ending in 5 is a multiple of 5 so is not prime. Primes > 5 end in 1, 3, 7 or 9. If n ends in 1, 1^4 is 1 so n^4 ends in a 1. If n ends in 3, 3^4 is 81 so n^4 ends in a 1. If n ends in 7, 7^4 is 2401 so n^4 ends in a 1. If n ends in 9, 9 4 is 6561 so n^4 ends in a 1. Statement proved by exhaustion