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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: ( Back to comment list | You must be logged in to post comments.)
solution | Comment 1 of 5

4 + 5 = 3^2

4^2 + 5^2 = 7^2

4^3 + 5^3 = 17^2

 


  Posted by Claire on 2008-04-22 09:38:42
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