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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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extended search | Comment 2 of 8 |
(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 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
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 2007-06-21 11:05:34
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