Quote:
Originally Posted by enzocreti
Are there other numbers N that can be written as (2^n4) and as (3*s^2+1)?

Quick piece of Mathematica code to test this:
Code:
For[n = 1, n <= 10000, n++,
If[IntegerQ[Sqrt[1/3*(2^n  5)]], Print[n, " ", 2^n  4]]]
This is equivalent since
Code:
2^n4=3s^2+1
2^n5=3s^2
s^2=1/3*(2^n5)
s = sqrt(1/3*(2^n5))
Up to n = 20000 there are 3 n's such that 2^n4 = 3s^2+1 for some integer s:
Code:
3 (corresponding to 4)
5 (28)
9 (508)