I have a task 50!+7^133 mod 5.
I know that 7^133(mod5)=2(mod5) because:
7=2(mod5)
7^2=4(mod5)
7^3=3(mod5)
7^4=1(mod5)
7^133= 7^(433+1)=(7^4)^337^1=1*2=2(mod5)
I'm not quite sure how can I calculate 50 in factorial. Any tips?
2026-04-12 18:55:42.1776020142
Fast modular exponentiation with factorial
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If $a \le b$ then $b! \equiv 0 \bmod a$.
In this problem, $50! \equiv 0 \bmod 5$.