mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Blogorrhea > enzocreti

Reply
 
Thread Tools
Old 2019-01-21, 10:15   #1
enzocreti
 
Mar 2018

17·31 Posts
Default 2^x-41

Are 8=x and 36=x the only integer values such that 2^x-41 is divisible by 215?
enzocreti is offline   Reply With Quote
Old 2019-01-21, 10:36   #2
paulunderwood
 
paulunderwood's Avatar
 
Sep 2002
Database er0rr

2×11×167 Posts
Default

Quote:
Originally Posted by enzocreti View Post
Are 8=x and 36=x the only integer values such that 2^x-41 is divisible by 215?
No. For example:

Code:
n=215;ph=eulerphi(n);e=8+ph*2^1000;r=Mod(2,n)^(e)-41;if(r==0,print(e))
  *** _^_: Warning: Mod(a,b)^n with n >> b : wasteful.
1800134460072929099193354082420803041743160083665296460505500652462189765889892685788573276410369041654359050501489286666314404079963087593245409032549360567061007386170470805550740533650478351835496302601711807797241766132922992949939811382940946569647961008251339084166952211717640896988650552235655176

For those values less than or equal to eulerphi(215):

Code:
n=215;ph=eulerphi(n);for(k=1,ph,r=Mod(2,n)^(k)-41;if(r==0,print(k)))
8
36
64
92
120
148

Last fiddled with by paulunderwood on 2019-01-21 at 10:55
paulunderwood is offline   Reply With Quote
Reply

Thread Tools


All times are UTC. The time now is 14:31.

Wed May 12 14:31:25 UTC 2021 up 34 days, 9:12, 0 users, load averages: 5.20, 4.83, 3.58

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.