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2022 OIM Problems/Problem 6

Problem

Let $\mathbb{Z}^+$ be the set of positive integers. Find all functions $f: \mathbb{Z}^+ \to \mathbb{Z}^+$ for which

\[f(a)f(a + b) - ab\]

is a perfect square for all $a, b$ in $\mathbb{Z}^+$


Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

https://sites.google.com/uan.edu.co/oim-2022/inicio

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