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Question

Find the remainder when 35! is divided by 37.

A
35
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B
37
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C
36
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D
1
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Solution

The correct option is D 1

From Wilson’s theorem, 36! (mod 37) = 36 , as 37 is a prime number.
(36 35!) (mod 37) = 36 36 (35! Mod 37) = 36

In order to have LHS = RHS, we need to have 35! (mod 37) = 1. Hence, 1 is the answer.


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