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Number Theory Level 3

If 1212 ! ≡ x ( m o d 1213 ) 1212! \equiv x \pmod{1213} , find the largest negative integer value of x x .


The answer is -1.

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Amar Mavi by Amar Mavi , 25, India

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1 solution

Mehul Arora
Feb 11, 2016

We observe that 1213 is a prime number

Using Wilson's theorem, if n is a prime number, then ( n − 1 ) ! ≡ − 1 ( m o d n ) (n-1)! \equiv -1 (mod n)

Thus the largest and only negative integer that can be x is − 1 -1

2 Helpful 0 Interesting 0 Brilliant 0 Confused

yes its right

Amar Mavi - 5 years, 4 months ago

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