20200224, 13:21  #1 
Mar 2018
2×263 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
2^{2}×11×107 Posts 
Don't forget 4

20200224, 13:56  #3 
Mar 2018
2·263 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
517_{10} 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) 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prime numbers test primality  with proof written in invisible ink  Godzilla  Miscellaneous Math  40  20181017 00:11 
any suitable sieve written in C or Python?  Shen  Information & Answers  4  20170105 04:49 
Looking for British written American history on Kindle  jasong  Homework Help  3  20150130 21:36 
ways to get rid of oil spills  science_man_88  Puzzles  9  20100730 21:22 
Math of LLR(written by Jean Penne)  TTn  15k Search  3  20060106 00:08 