let's consider x = k.z +y then how can we define the set of integers modulo z? and what does set of integers modulo z mean?

I am a programmer and I try to understand these things so could any body help me.

I found this example

The Set Of Integers Modulo P The set:

Zp={0,1,2,...,p−1}(1) Is called the set of integers modulo p (or mod p for short). It is a set that contains Integers from 0 up until p−1.

Example: Z10={0,1,2,3,4,5,6,7,8,9}

but I do not know why the call that set as set of integers modulo p


closed as off-topic by graydad, Harish Chandra Rajpoot, Batominovski, Michael Galuza, user223391 Aug 15 '15 at 5:48

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  • $\begingroup$ Doing addition, subtraction, or multiplication modulo $z$ means doing the operation the usual way, then dividing by $z$, throwing away the quotient, and reporting only the remainder. For example, doing $6\times7$ modulo $10$, you do $6\times7=42$, $42$ divided by $10$ is $4$, remainder $2$, so the answer is $2$. $\endgroup$ – Gerry Myerson Aug 15 '15 at 0:35
  • $\begingroup$ There are probably thousands of existing resources online about the definition of modulo, including Wikipedia. Have you looked at any of them? $\endgroup$ – epimorphic Aug 15 '15 at 0:44
  • $\begingroup$ I have edited my question it could be clearer now! $\endgroup$ – user3260672 Aug 15 '15 at 1:13

Simply put, to consider the integers modulo $z$ is to take the entire set of integers $\{0,-1,1,-2,2,\cdots\}$, divide everything by $z$, and consider only the remainders.

Therefore "the set integers modulo $z$" is the set of all possible remainders upon division by $z$, which is $\{0,1,\cdots,z-1\}$.

Is this clear?

  • $\begingroup$ thanx a lot.... $\endgroup$ – user3260672 Aug 15 '15 at 1:20

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