Find the least nonnegative residue of 2(100!) modulo 103

This is what I have so far but dont know where to go form here:

2(100!)x≡1 mod 103

2(100!)x≡104 mod 103

100!x≡52 mod 103

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- Oct 7th 2008, 11:41 AM #1

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- Oct 7th 2008, 11:48 AM #2

- Oct 7th 2008, 12:13 PM #3

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- Oct 7th 2008, 12:22 PM #4
Yeah I know, it's a real mess...

Keep in mind that we want to find x in

We know that , that is to say

But

So

So if I can reduce , it would be nice !

101 is 103-2, so writing it this way will make appear 103.

Hence, if we go back to the boxed expression, we'll get :

But we know that (1)

Therefore