- #1

steiner1745

- 1

- 0

I got this question from another

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?

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?

Last edited: