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MathNet 2010 — Part 03 Question 199

Math Olympiad Vault · MathNet 2010 — Part 03

Question 199

Find all positive integers $n$ which satisfy the following two conditions:
(i) $n$ has at least four different positive divisors;
(ii) for any divisors $a$ and $b$ of $n$ satisfying $1 \lt a \lt b \lt n$, the number $b - a$ divides $n$.