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Math · Advanced Math
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Proposition 3.11. Addition and multiplication modulo n are associative. Proof. Both a tn (b tn ) and (a nb n c are equal to the remainder of a + b+ c on division by n. To see this, observe first that if p,q E N and p q+ kn for some k then atnp atn g. This is easy to see. It follows in particular that a tn (btn c) - a+n (b+ which is equal, by definition, to the remainder of a+b+ c after dividing by n. The same argument shows that (a tnb) +i c is equal to the remainder of a +b+ c on division by n. The argument for multiplication is similar: both a XnbxnC) and (a xn b) Xn c are equal division by n. I leave this for you to show.

Can you explain the process of the proof for me?

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