Question 98
Prove that for every positive integer $n$ there are at most two pairs $(a, b)$ of positive integers with the following two properties:
(i) $a^{2}+b=n$,
(ii) $a+b$ is a power of two, i.e. there is an integer $k \geq 0$ with $a+b=2^{k}$.
(i) $a^{2}+b=n$,
(ii) $a+b$ is a power of two, i.e. there is an integer $k \geq 0$ with $a+b=2^{k}$.