Ive got this assignment for uni where I need to prove the following:
We have a set of $16$ different positive integers $\leq 100$, prove that there are always $a,b,c,d$ in this set so that $a + b = c + d$.
I think this is to be solved with the pigeonhole principle, but I cant quite figure it out. Does anyone know how this could be done?
Any help would be appreciated!!