When 35! is divided by 37, find the remainder.

Jazlyn Durham

Jazlyn Durham

Answered question

2023-01-15

When 35! is divided by 37, find the remainder.
A) 35
B) 37
C) 36
D) 1

Answer & Explanation

eggnogwxb

eggnogwxb

Beginner2023-01-16Added 6 answers

The correct answer 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. Therefore, 1 is the answer.

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