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Show that exists positive integer

Source: 67 Polish MO 2016 Second Round - Problem 4

April 30, 2018
number theorysetPerfect SquaresPoland

Problem Statement

Let kk be a positive integer. Show that exists positive integer nn, such that sets A={12,22,33,...}A = \{ 1^2, 2^2, 3^3, ...\} and B={12+n,22+n,32+n,...}B = \{1^2 + n, 2^2 + n, 3^2 + n, ... \} have exactly kk common elements.
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