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 computer-aided 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 2014-12-18 13:00:57