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For some integers a,b, a=b (mod x). Find x in terms of a and b.

It appears the answer is a-b, but I'm not sure how to prove it without modular arithmetic, which I don't really understand.

Is there a simple way to prove and explain this without mods?

 Dec 7, 2018
 #1
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What I'm seeing is that if you take the prime factors of (a-b) as a set

 

And take all length permutations of that set and then take the product of the elements in that permutation

 

All those values will be values of x such that a = b mod x

 

I don't know of any way to show this without using any modular arithmetic at all.

 Dec 7, 2018
 #3
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I see, thanks anyways!

Guest Dec 7, 2018
 #2
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[deleted]

 Dec 7, 2018
edited by Guest  Dec 7, 2018

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