Find all possible triplets (A,B,C) of positive integers that satisfy the following system of equations:
A^{2} = 2(B+C) and:
A^{6} = B^{6} + C^{6} + 31(B^{2} +C^{2})
If you cube the first equation you can substitute
A^{6 }in the second:
8(B+C)^{3} = B^{6} + C^{6} + 31(B^{2} +C^{2})
When I entered this into WolframAlpha the graph is a rather small egg shape with the blunt end at b=1, c=1 and narrow end around b= 2.75, c=2.75
There are solutions very near (2,1) and (1,2) but not quite.
The only positive integer solution is (A,B,C)=(2,1,1).

Posted by Jer
on 20150605 11:08:59 