1. The problem statement, all variables and given/known data Show that in any set of 172 integers there must be a pair whose difference is divisible by 171. Is the result true if the word difference is replaced by sum. I think it should say distinct integers 3. The attempt at a solution I think I should start by partitioning the integers into segments from 1 to 171 and then multiples of 171 like n171 I guess you would have a case where some of the integers could be multiples of 171 and then their difference would be divisible by 171. Or you would have them scattered in between some multiple of 171 , but we have 172 of them and there are only 170 numbers in between any multiple of 171 so their should exist a pair whose difference is a multiple of 171. is this on the right track, i need o quantify this a little more.