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MathNet 2016-part-06 — 184 problems (EN–VI) Question 44

Math Olympiad Vault · MathNet 2016-part-06 — 184 problems (EN–VI)

Question 44

Let $m \ge 1$ be a positive integer, and let $a$ and $b$ be distinct positive integers strictly greater than $m^2$ and strictly less than $m^2 + m$. Find all integers $d$ that divide the product $ab$ and satisfy $m^2 \lt d \lt m^2 + m$.