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2022 OIM Problems/Problem 6

Revision as of 03:45, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>\mathbb{Z}^+</math> be the set of positive integers. Find all functions <math>f: \mathbb{Z}^+ \to \mathbb{Z}^+</math> for which <cmath>f(a)f(a + b)...")
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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

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See also

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

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