I got this question from another(adsbygoogle = window.adsbygoogle || []).push({});

forum and it's driving me crazy.

Find all triples of odd primes,

p,q,r such that

p^2+1 is divisible by q, q^2+1 is divisible by r

and r^2+1 is divisible by p.

Two such triples are 5,13,17

and 17,29,421. If we assume

p<q<r, then there are no other

such triples with p<10^7.

Are there any others?

Anyone have any ideas?

From quadratic residue theory

we know that p,q,r are all

congruent to 1(mod 4).

Can we say more?

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# A ring of odd primes

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