If y=4 and z=10, then what are the set of integers modulo z? [closed]

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – graydad, Harish Chandra Rajpoot, Batominovski, Michael Galuza, Community
If this question can be reworded to fit the rules in the help center, please edit the question.

• 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 $2$. – Gerry Myerson Aug 15 '15 at 0:35
• There are probably thousands of existing resources online about the definition of modulo, including Wikipedia. Have you looked at any of them? – epimorphic Aug 15 '15 at 0:44
• I have edited my question it could be clearer now! – 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 $\{0,1,\cdots,z-1\}$.