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October 1st, 2018, 04:51 AM   #1
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Modulo negative integer

Why can't we have modulo negative number? I have never seen this.
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October 1st, 2018, 04:57 AM   #2
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Math Focus: Yet to find out.
Why not?

https://math.stackexchange.com/quest...egative-number
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October 1st, 2018, 05:02 AM   #3
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Quote:
Originally Posted by Joppy View Post
I think he means something like 2 module -3.

This is indeed very uncommon, but it is entirely well-defined.

Notice that x=y mod N if and only if N divides x-y. But N divides x-y if and only if -N divides x-y.

So modulo -N is the same as modulo N.

Even modulo 0 and modulo 1 are well-defined. The integers modulo 0 are just the integers themselves, for example.
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