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#1 2017-11-14 07:04:18

ATD
Guest

A hard modular arithmetic problem

Could you please help me with this problem:

20! * 12! = x (mod 2012)

Some useful facts i have discovered:

1)    7 * 8 * 9 = 1 (mod 503)

2)   20! * 12! = 13 * 17 * 19 mod(503)

I have been trying to solve this problem for a long time. If you can find the answer, could you please show the step by step solution? Thank you for your help.

#2 Today 10:44:16

Alg Num Theory
Member
Registered: Today
Posts: 5

Re: A hard modular arithmetic problem

By direct calculation,

12! = 479001600 ≡ 736 (mod 2012),
20! = 2432902008176640000 ≡ 344 (mod 2012);

20!×12! ≡ 344×736 = 253184 ≡ 1684 (mod 2012).

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