(In reply to
re: Start by broll)
From Google I learn that Fermat studied the curves x^3+y^3=Az^3 an stablish that if there is a non trivial solution then exists infinitely many.
Prestet working on Fermat get some formulas to obtain other solutions from one:
X=x(2y^3+x^3), Y=y(2x^3+y^3), Z=z(x^3y^3)
Using our solution (137, 65, 42) we get:
(277028111, 316425265, 119531076), all positive integers.
Then:
X+Y+Z= 712984452
and
31Z^3=5.2942468*10^25
I'm not sure this is the smallest value, but Charlie's search makes it quite possible.
Edited on April 23, 2016, 9:39 am

Posted by armando
on 20160423 09:37:45 