Find, with proof, the minimum positive integer n with the following property: for any coloring of the integers {1, 2, . . . , n} using the colors red and blue (that is, assigning the color “red” or “blue” to each integer in the set), there exist distinct integers a, b, c between 1 and n, inclusive, all of the same color, such that 2a + b = c.

broww Sep 12, 2021