perplexus.info :: Numbers : Prime Pairs satisfy Quintic = Cubic

Prime Pairs satisfy Quintic = Cubic (Posted on 2024-02-17)

Given that each of p and q is a prime number:

Determine all possible pairs (p,q) that satisfy this equation:

        p(p⁴+p²+10q) = q(q²+3)

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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probable solution

| Comment 1 of 7

clearvars

qset=primes(100000);

pset=primes(1000);

for p=pset

for q=qset

if p^5 + p^3 + 10*p*q == q^3 + 3*q

disp([p q])

end

finds only (2,5) having tested all 168 primes under 1000 for p, and all 9592 primes under 100,000 for q.

Posted by Charlie on 2024-02-17 15:52:16

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