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?

The problem with the fourth powers is an old one, supposedly asked by Hardy to Ramanujan, after the latter commented that 1729= 9^3+10^3 =1^3+12^3; the answer is 635318657= 59^4+158^4= 133^4+134^4
Edited on February 6, 2004, 8:54 am

Posted by e.g. on 2004-02-06 08:51:39