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Sum of Powers (Posted on 2008-04-21) Difficulty: 4 of 5
The numbers 184 and 345 have a special property. Their sum, the sum of their squares, and the sum of their cubes are all perfect squares:
184 + 345 = 23^2
184^2 + 345^2 = 391^2
184^3 + 345^3 = 6877^2

Find another primitive pair of non-zero integers with the same property. Note, a primitive solution is a solution which is not a multiple of any smaller solution.
If you have extended precision math software, try to find a third or fourth primitive solution.

Tip: one of the numbers may be negative.

No Solution Yet Submitted by Brian Smith    
Rating: 4.0000 (2 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
thoughtsPaul2008-04-24 07:38:36
Some ThoughtsDiophantine ThoughtsK Sengupta2008-04-24 06:08:08
Hints/TipsSolving tipsBrian Smith2008-04-24 00:42:31
re: solutionPraneeth2008-04-22 09:52:47
solutionClaire2008-04-22 09:38:42
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