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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?

  Submitted by SilverKnight    
Rating: 2.5000 (2 votes)
Solution: (Hide)
1729 = 1³ + 12³ = 9³ + 10³
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635,318,657 = 59^4 + 158^4 = 133^4 + 134^4
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Charlie posted a comment containing program that determines these and the next few solutions.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(4): A way to do it.===> NO WAY, not quiteFrank Riddle2004-02-25 23:42:14
Some Thoughtsre(3): A way to do it.===> NO WAY, not quiteAdy TZIDON2004-02-25 04:20:09
re(2): A way to do it.===> NO WAYFrank Riddle2004-02-24 21:33:04
re(2): Hardy's StoryRichard2004-02-09 12:58:27
re: Hardy's StoryPenny2004-02-09 01:27:22
re: A way to do it.===> NO WAYAdy TZIDON2004-02-07 04:05:04
Hardy's StoryRichard2004-02-06 16:17:23
A way to do it.Gamer2004-02-06 15:06:51
re: QuestionSilverKnight2004-02-06 13:50:01
QuestionQuestionPenny2004-02-06 13:40:27
Hints/Tipsre(2): LOLe.g.2004-02-06 11:56:39
re: LOLSilverKnight2004-02-06 10:42:59
LOLnikki2004-02-06 10:05:48
SolutionsolutionCharlie2004-02-06 09:30:25
SolutionOld probleme.g.2004-02-06 08:51:39
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