Let
m and n be integers each less than
2014.
Determine the maximum value of
m^3+n^3 fulfilling the equation
(n^2  mn  m^2)^2 = 1
(In reply to
computeraided solution by Charlie)
Seeing this solution it is very easy to show that if m=1,n=1 works then any Fibonacci numbers work.
Replace n with m and m with m+n and the expression simplifies to the original.
You can also show that if m, n works then n,m works.
That doesn't, or course, rule out any other solutions. Charlie's program found none, so I'll leave it at that.

Posted by Jer
on 20141218 13:00:57 