Determine all possible triplet(s) (P, Q, R) of nonnegative integers, with P ≥ Q, such that each of P² + 1 and Q² + 1 is a prime, and: (P² + 1)(Q² + 1) = (R² + 1).

 10   for T=1 to 10000
 20    for Q=1 to int(T/2)
 30      P=T-Q
 40      Q1=Q*Q+1:P1=P*P+1
 50        if prmdiv(Q1)=Q1 then
 70          :if prmdiv(P1)=P1 then
 80             :R=int(sqrt(P1*Q1-1)+0.5)
 90             :if R*R+1=P1*Q1 then
100              :print P;Q;R
110    next
120   next

Tests all P and Q whose sum is 10,000 or less and finds only (2, 1, 3)

Posted by Charlie on 2009-08-16 16:50:32