What is the smallest positive integer that is the sum of two different pairs of (non-zero, positive) cubes?
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What is the smallest positive integer that is the sum of two different pairs of integers raised to the 4th power? and how did you find it?

In other words what is the smallest x such that:
x = a^4 + b^4 = c^4 + d^4
(where x, a, b, c, and d are all different, non-zero, positive integers)?
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Are you able to determine the answer without looking it up on the internet?

How the heck did Ramanujan find the answer so quickly? (Unless he had previously brute-forced it...and he didn't have a computer).

Sometimes extraordinary geniuses are capable of amazing mental feats. Von Neuman, one of the fathers of the modern computer, once solved the old "zig-zagging fly" brain-teaser by instantly solving a difficult differential equation in his head.



Edited on February 6, 2004, 1:44 pm

Posted by Penny on 2004-02-06 13:40:27