Suppose $f:\mathbb{Z}^+\longrightarrow X$ is a function, with $X$ a finite set. Is it true that there are $a,b\in\mathbb{Z}^+$ such that $f(a)=f(b)=f(a+b)$.
2026-03-28 04:01:46.1774670506
Coloring of positive integers
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I believe, though I am not sure, this is what you are looking for: http://books.google.com/books?id=hUGxm9RdTeUC&pg=PA4&lpg=PA4&dq=schur+coloring+of+positive+integers&source=bl&ots=IrYWq_eBSY&sig=wkWhM0nQfCAbAGPCZFoYDHwRYFE&hl=en&sa=X&ei=sWaTUKGjOITk0QHSq4HoBQ&ved=0CE0Q6AEwBw#v=onepage&q=schur%20coloring%20of%20positive%20integers&f=false
Please correct me if I am wrong. This is not something I am familiar with, but is nonetheless very interesting.