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?

Hardy, after telling the "1729" part of the story (1729 was the cab number Hardy had ridden to visit Ramanujan) then adds "I asked him, naturally, whether he could tell me the solution of the corresponding problem for fourth powers; and he replied, after a moment's thought, that he knew no obvious example, and supposed that the first such number must be very large." I have copied this from Hardy's "Ramanujan" where Hardy is quoting from his own memoir of Ramanujan that he contributed to Ramanujan's "Collected Papers."
Edited on February 6, 2004, 10:31 pm

Posted by Richard on 2004-02-06 16:17:23