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Multiply Together, Get Cubic (Posted on 2007-06-21) Difficulty: 4 of 5
Determine all possible integer pairs (p,q) such that p+q+s=pqs, where s=gcd(p,q) and gcd denotes the greatest common divisor.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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early results -- no proof | Comment 1 of 8

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
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