because 31 is prime we have as per wilson's theorem
30! \equiv -1 (\,mod\, 31)\cdots(1)
and also 30 * (-1) = -30 \equiv 1 (\,mod\, 31) =>30^{-1} = \equiv 1 (\,mod\, 31)\cdots(2)
from (1) and (2)
29! \equiv 1 (\,mod\, 31)
or 4 * 29! \equiv 4 (\,mod\, 31)
or 4 * 29! + 5! \equiv 4 + 120 (\,mod\, 31) \equiv 124 (\,mod\, 31) \equiv 0 (\,mod\, 31)
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