Show that given 52 integers there are two of them whose sum or difference is divisible by 100.
Can someone show this using the pigeon hole principle please. Thanks!!
Note that if one considers the residue classes and the - residue classes there are $\displaystyle 52\cdot 2-1$ distinct ones where the subtraction of one was given since the residue class $\displaystyle [0]$ is equal to it's negative. Conclude.