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.

(In reply to solution by broll)

2 questions:

1. How do we know it is the minimal solution?

2. Why the wording of  (i)  is different from wordings of  (ii and (iii)?

Posted by Ady TZIDON on 2015-07-30 12:30:37