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A ring of odd primes 
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#1
Jul211, 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? 


#3
Jul611, 10:26 PM

P: 460

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. 


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