A ring of odd primes

by steiner1745
Tags: primes, ring
steiner1745 is offline
Jul2-11, 09:28 PM
P: 1
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?
Phys.Org News Partner Science news on Phys.org
Better thermal-imaging lens from waste sulfur
Hackathon team's GoogolPlex gives Siri extra powers
Bright points in Sun's atmosphere mark patterns deep in its interior
micromass is online now
Jul6-11, 01:15 PM
micromass's Avatar
P: 16,543
(2,5,13) also works...
agentredlum is offline
Jul6-11, 10:26 PM
P: 460
Quote Quote by micromass View Post
(2,5,13) also works...
nice observation but 2 is not an odd prime.

Years ago i thought i solved the BEAL CONJECTURE because i found 3^5 + 10^2 = 7^3

Then my math prof. pointed out ALL exponents must be integers greater than 2.

Register to reply

Related Discussions
Compatible ring structure on ring-valued set functions Calculus & Beyond Homework 2
Pythagorean Primes and Gaussian Primes, divisibility question Linear & Abstract Algebra 3
Thompson's Jumping Ring with the ring in the centre of the solenoid Introductory Physics Homework 0
Finding the B-field at a point outside ring of current IN Plane of ring Introductory Physics Homework 1
Primes in ring of Gauss integers - help!! Linear & Abstract Algebra 7