Question 1166868
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The post / (the condition) is  FATALLY  INCOMPLETE,  since it does not determine what the set  N  is.


The standard designation for the set of integer numbers is  Z;


so,  based on the post,  the set of numbers in this problem is not  Z;


then  WHAT  it is ?



It is a typical case at this forum,  when the person who creates / (composes)  the problem,

does not know the subject and does not know  WHAT  he  (or she)  writes about and how to write it correctly.



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From Wikipedia,  the free encyclopedia  

https://en.wikipedia.org/wiki/Binary_operation#:~:text=In%20mathematics%2C%20a%20binary%20operation,operands)%20to%20produce%20another%20element.&text=Examples%20include%20the%20familiar%20arithmetic%20operations%20of%20addition%2C%20subtraction%2C%20multiplication.



<pre>
    In mathematics, a binary operation or dyadic operation is a calculation that combines two elements (called operands) 
    to produce another element. More formally, a binary operation is an operation of arity two.

    More specifically, a binary operation on a set is an operation whose two domains and the codomain are the same set. 
    Examples include the familiar arithmetic operations of addition, subtraction, multiplication. 
    Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication and conjugation in groups.
</pre>