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Power Difference Puzzle (Posted on 2015-07-30) Difficulty: 3 of 5
Find the minimum value of a positive integer N that simultaneously satisfy all the three conditions given below:

(i) N is expressible as the difference of two perfect squares.
(ii) N is expressible as the difference of two positive perfect cubes.
(iii) N is expressible as the difference of two positive perfect fifth powers.

No Solution Yet Submitted by K Sengupta    
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Solution solution | Comment 2 of 3 |
39^2-23^2=10^3-2^3=4^5-2^5; other pairs of squares also satisfy the equality.
  Posted by broll on 2015-07-30 10:52:25
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