Problem 57477. Solve an equation involving primes and fractions

Write a function to find pairs of primes p and q satisfying the equation
p/(p+1) + (q+1)/q = 2n/(n+2)
where n is an integer. The function should take a number x as input and produce the triples p, q, and n such that p <= x. If there are no solutions, the function should return three empty vectors.
This problem is adapted from one in the 2012 European Girls’ Math Olympiad.
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Solution Stats

52.38% Correct | 47.62% Incorrect
Last Solution submitted on Dec 14, 2025

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