Numbers that can be written in two different ways
4, 28 and 508 can be written as (2^n4) for some n, but also as:
(3*s^2+1) for some s Are there other numbers N that can be written as (2^n4) and as (3*s^2+1)? 
Don't forget 4

...primes...
5, 29, 509 are primes
such that can be written as 3*n^2+2 and as 2^s3 for some n and s do you believe they are infinite? 
[QUOTE=enzocreti;538250]
Are there other numbers N that can be written as (2^n4) and as (3*s^2+1)?[/QUOTE] 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]]][/CODE]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))[/CODE] 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)[/CODE] 
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