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MathNet 2026 — Part 03 Question 176

Math Olympiad Vault · MathNet 2026 — Part 03

Question 176

We say that a set $E$ of natural numbers is special when taking any two different elements $a, b \in E$ has that $(a-b)^2$ divides the product $ab$.
a. finds a special set made up of three elements.
b. Is there a special set formed by four natural numbers that are in arithmetic progression?