Let p > q be primes, such that 240 p^4 - q^4. Find the maximal value of qp. (Angel Gushev)

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Bulgarian Winter Tournament

Bulgaria number theory

Problem

Let

p > q

be primes, such that

240 ∤ p^{4} - q^{4}

. Find the maximal value of

\frac{q}{p}

. (Angel Gushev)

Solution

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Final answer

5/7

Techniques

Prime numbersFermat / Euler / Wilson theorems