I have a homework question that asks the following:
How many order pair of integers (a,b) are needed to guarantee that there are two ordered pairs (a1,b1) and (a2,b2)such that such that a1 mod 5= a2 and b1 mod 5= b2?
I know that this is a pigeonhole principle question and I searched for the question online, but I didn't quite understand the answer. My question is: what does it mean for integers such as k and q, such that k mod 5= q mod 5? And can someone explain how to solve this? I just want to understand; I don't care about getting the answer us much as I care about learning how to do this.