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Cubic AND Quartic Challenge (Posted on 2004-02-06) Difficulty: 4 of 5
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?

See The Solution Submitted by SilverKnight    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
A way to do it. | Comment 8 of 15 |
The cube thing could be done more easily than it seems. If you ever saw the cube root of 12, 1728, you could think "Wow; if you add the one at the beginning to the end, it's also a perfect cube", then you would be set up for knowing the answer.
  Posted by Gamer on 2004-02-06 15:06:51
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