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An old polynomial bijection between N and NxN

Source: Germany 2019, Problem 4

June 20, 2019
algebrapolynomialnumber theory

Problem Statement

Show that for each non-negative integer nn there are unique non-negative integers xx and yy such that we have n=(x+y)2+3x+y2.n=\frac{(x+y)^2+3x+y}{2}.
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