Question

Find the remainder when 35! is divided by 37.

• A. 35
• B. 37
• C. 36
• D. 1

Answer 1

The correct option is D 1

From Wilson’s theorem, 36! (mod 37) = 36 , as 37 is a prime number.
(36 ${}^{\ast }$ 35!) (mod 37) = 36 $\Rightarrow$ 36 ${}^{\ast }$ (35! Mod 37) = 36
In order to have LHS = RHS, we need to have 35! (mod 37) = 1. Hence, 1 is the answer.