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
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 Tot-1
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
(the gcd always is considered positive)
Posted by Charlie
on 2007-06-21 11:05:34