Witty Wilson

Number Theory Level 1

What is the remainder when 18 ! 18! is divided by 19?


Notation : ! ! denotes the factorial notation. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .


The answer is 18.

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Yash Jain by Yash Jain , 21, India

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2 solutions

Applying Wilson's theorem as 19 is prime, ( 19 − 1 ) ! ≡ − 1 ≡ 18 ( m o d 19 ) (19-1)!\equiv -1\equiv 18(mod\quad 19)

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Prokash Shakkhar
Dec 10, 2016

By Wilson's Theorem, As 19 is prime.. So, ( 19 − 1 ) ! ≡ − 1 ≡ 18 ( m o d 19 ) (19-1)!\equiv -1\equiv 18\pmod{19}

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how to solve 37! mod 41 then

Walter White - 7 months ago

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