What is the meaning of this expression ?

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The expression nZ/mZ represents a quotient group where n and m are integers, and Z denotes the set of all integers. When n=1, Z/mZ simplifies to the set of integers modulo m, specifically {0, 1, 2, ..., m-1}. For m=2, this corresponds to a binary system. The discussion emphasizes that n must divide m for the quotient to be valid, resulting in an isomorphic structure Z/m'Z, where m=nm'. Although the cosets differ, they maintain isomorphism.

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nZ/mZ

where / means a quotient group

if n=1 then Z/mZ is the set of integers modulus n {0,1,2,3,4,...,n-1} in case

m=2 we have a binary system, but i do not know what (1) will mean

of ocurse 'Z' means the set of all (positive) integers.
 
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What is (1)?

Anyway, this only makes sense if n divides m as you need mZ to be a subgroup of nZ.

In this case you can just factor n out and be left with something isomorphic to Z/m'Z where m=nm'.

They are not equal - the the cosets are different but they are isomorphic.
 

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