20200224, 13:21  #1 
Mar 2018
17·31 Posts 
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)? Last fiddled with by enzocreti on 20200224 at 13:51 
20200224, 13:29  #2 
Jun 2003
17×281 Posts 
Don't forget 4

20200224, 13:56  #3 
Mar 2018
20F_{16} Posts 
...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? 
20200224, 17:59  #4  
"Dylan"
Mar 2017
1000010000_{2} Posts 
Quote:
Code:
For[n = 1, n <= 10000, n++, If[IntegerQ[Sqrt[1/3*(2^n  5)]], Print[n, " ", 2^n  4]]] Code:
2^n4=3s^2+1 2^n5=3s^2 s^2=1/3*(2^n5) s = sqrt(1/3*(2^n5)) Code:
3 (corresponding to 4) 5 (28) 9 (508) 

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