# Math Help - Proof using wilson's method, I believe

1. ## Proof using wilson's method, I believe

How would I prove that 4(29!) + 5! is divisible by 31?

2. Originally Posted by MichaelG
How would I prove that 4(29!) + 5! is divisible by 31?

Modulo 31 we have $4(29!)+5!=\frac{4(30!)}{30}=\frac{4(-1)}{-1}+5!=4+4!\cdot 5=4+24\cdot 5=4+(-7)5=4-35=-31$

Tonio