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Problem 1319

AIME late

Number theory Difficulty 5.1 Prove it Bulgarian Winter Tournament · Bulgaria

Let $p > q$ be primes, such that $240 \nmid p^4 - q^4$ . Find the maximal value of $\frac{q}{p}$ .
(Angel Gushev)

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

Official solution

$\square$

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