Determine all possible integer pairs (p,q) such that p+q²+s³=pqs, where s=gcd(p,q) and gcd denotes the
greatest common divisor.
(In reply to
early results  no proof by Charlie)
For positive and negative p and q up to abs(p)+abs(q) = 38,000, the same set of four were the only ones found.
10 for Tot=3 to 1000000
20 for P=1 to Tot1
30 Q=TotP
40 S=gcd(P,Q)
50 if P+Q*Q+S*S*S=P*Q*S then print P;Q
51 if P+Q*Q+S*S*S=P*Q*S then print P;Q
52 if P+Q*Q+S*S*S=P*Q*S then print P;Q
53 if P+Q*Q+S*S*S=P*Q*S then print P;Q
60 next
70 next
(the gcd always is considered positive)

Posted by Charlie
on 20070621 11:05:34 