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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.)
Hints/Tips re(2): LOL | Comment 5 of 15 |
(In reply to re: LOL by SilverKnight)

I followed the letter of the problem, and didn't use a computer -- not for calculating, not for web surfing.

What I *did* use was a book I had, "Elementary Theory of Numbers"...


(signed)
Someone
  Posted by e.g. on 2004-02-06 11:56:39

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