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bw painting integers, m white => m + 20 white, k black => k + 35 black

Source: Norwegian Mathematical Olympiad 2012 - Abel Competition p1b

September 4, 2019
number theorycombinatoricsColoring

Problem Statement

Every integer is painted white or black, so that if mm is white then m+20m + 20 is also white, and if kk is black then k+35k + 35 is also black. For which nn can exactly nn of the numbers 1,2,...,501, 2, ..., 50 be white?
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