Prove the divisibility of the following numbers by 7 5 {}^(5) - 5 {}^(4) + 5 {} {}^(3) \:

Question

Prove the divisibility of the following numbers by 7


`5 {}^(5) - 5 {}^(4) + 5 {} {}^(3) \:`

Answer 1

5^5 mod 7 = 3
5^4 mod 7 = 2
5^3 mod 7 = 6

3 -2 +6 mod 7 = 0
Therefore, 5^5 -5^4 +5^3 mod 7 = 0 and that sum is divisible by 7.