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Question
What is the remainder when 50! Is divided by 47^2 ? Please explain it by using wilson theorem.
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Answer
47 is a prime number. So, 46! mod 47 = 46
50! mod 47^2 = 50*49*48*47*46! mod 47^2
= 47*(50*49*48*46! mod 47)
50 mod 47 = 3
49 mod 47 = 2
48 mod 47 = 1
46! mod 47 = 46
So, the expression becomes 47*(3*2*1*46 mod 47) = 47*(276 mod 47) = 47*41 = 1927
