How would I prove that 4(29!) + 5! is divisible by 31?
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Originally Posted by MichaelG How would I prove that 4(29!) + 5! is divisible by 31? Modulo 31 we have $\displaystyle 4(29!)+5!=\frac{4(30!)}{30}=\frac{4(-1)}{-1}+5!=4+4!\cdot 5=4+24\cdot 5=4+(-7)5=4-35=-31$ Tonio
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