(In reply to An observation.
When I looked at this initially I wondered about "non zero real triplet(s)".
I did consider negatives, -2, -3 and -6. That gives the appropriate 2401=2401 for the first equation but leaves us with a -1 for the second.
Having one or two negatives, and then trying to equate to 1 in the second equation creates an imbalance in the first.
From my spreadsheet I determine F=2, G=3 and H=6.
Posted by brianjn
on 2012-07-30 23:08:45