r-color Schur numbers are the smallest integers, denoted as $$S_r(n)$$, such that if the integers from 1 to $$S_r(n)$$ are colored using r different colors, there exists a monochromatic set of n integers that forms an arithmetic progression. This concept expands on the classical Schur's theorem, which deals with monochromatic subsets in general and explores how coloring affects the presence of arithmetic progressions in different contexts.
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