MathDB
a^2 + b = n, a+b = 2^k for each positive integer k

Source: Dutch BxMO TST 2019 p1

January 10, 2020
number theory

Problem Statement

Prove that for each positive integer nn there are at most two pairs (a,b)(a, b) of positive integers with following two properties: (i) a2+b=na^2 + b = n, (ii) a+ba+b is a power of two, i.e. there is an integer k≥0k \ge 0 such that a+b=2ka+b = 2^k.
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