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.

For positive p and q, where p+q is under 21,000, only

 (4,  2)
 (5,  2)
 (5,  3)
 (4,  6)

work.

10 for tot = 3 to 1000000
20 for p=1 to tot-1
30 q=tot-p
40 s=gcd(p,q)
50 if p+q*q+s*s*s = p*q*s then  print p;q
60 next
70 next

Posted by Charlie on 2007-06-21 09:49:24