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.

(i)   N is expressible as the difference of two      perfect cubes.

does not say   two positive perfect cubes,

 so  N = K^2     fits the description,  since  N = K^2-0^2

Now find such N that fulfills cond (i) & cond (ii) .

Edited on July 30, 2015, 9:48 am

Posted by Ady TZIDON on 2015-07-30 09:42:08