(I) Consider two positive integers x and y with x < y < 2011 and, determine the minimum value of a positive integer constant n satisfying: x³ + y³ = 2011³ + n

(II) Keeping all the other conditions in (I) unaltered, determine the minimum value of n satisfying: x³ + y³ + n = 2011³

1248^3 + 1836^3 = 2011^3 + 2717

733^3 + 1978^3 + 1142 = 2011^3

I can only make scatterplots with about 500 points max.
Can someone make one of x vs n (with whatever y makes n closest to 0)?  It appears to have some quite interesting features.

Posted by Jer on 2011-11-02 10:56:13