- #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: