Determine all possible pair(s) (s,t) of integers that satisfy this equation:

2s³ = 3t² + 4

list
   10   for S=2 to 10000000
   20     Sum=2*S^3
   30     T=int(sqrt((Sum-4)/3)+0.5)
   40     if 3*T*T+4=Sum then print S;T;Sum
   50   next
OK
run
 2  2  16
OK

So for S up to ten million, (2,2) and its ancillary (2,-2) as noted by Dej Mar are the only solutions.

Posted by Charlie on 2009-06-13 19:38:17