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.

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