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I am a bit confused about modular arithmetic. We say that two integers are equal modulo n if their difference is an integer multiple of n.

So let's take as example: $5(mod2) = 1$, since $5-1 = 4$ which is an integer ($k$) multiple of 2.

But isn't this also true then: $5(mod2) = 3$? Because $5-3 = 2$ which is also an integer multiple of 2, namely $k=1$. If this is true, then why does a calculator just give $5(mod2) = 1$?

Same for $-2(mod7)=5$, why do we pick 5 if there are infinitely many equalities?

Stallmp
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    You are confusing mod the remainder operation with mod the congruence relation - a common source of confusion . See e.g. here in the dupe for further elaboration. Please delete the question once all is clear. – Bill Dubuque Mar 24 '24 at 13:52

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