20200412, 14:04  #1 
Apr 2020
2 Posts 
One Theorem about Mersenne Numbers
All composite factors of primeexponent Mersenne Numbers are strong pseudoprimes to base 2. However, I have a problem. How can I prove this theorem?

20200412, 18:13  #2  
Feb 2017
Nowhere
3×1,153 Posts 
Quote:
This is elementary number theory. Let p > 2 be a prime number. Every factor n > 1 of 2^p  1 (whether prime or composite) is congruent to 1 (mod p). Therefore p divides n1, so 2^{p}  1 divides 2^{n1}  1, so n divides 2^{n1}  1. Let o be the odd part of n1. Then p divides o. So 2^{o} == 1 (mod n). Last fiddled with by Dr Sardonicus on 20200413 at 00:23 Reason: transcription error 

20200413, 04:23  #3 
Romulan Interpreter
Jun 2011
Thailand
2×11×397 Posts 
Grrr... couldn't you choose some other variable* instead of that "o"? Quite confusing with zero, (not only for beginners )
On the other hand, this is indeed more like for the homework subforum, it should be moved there.  *On the funny side, I had a colleague in middle school who called all variables in equations "ț" (this is pronounced as the German "tz" group and at the time we were studying first and second degrees equations, and linear systems with few equations). He was good in math, and he wanted to follow a career in computer science, but when he found out that the keyboard has no ț (at the time, it was not possible to type ț, thingies like "word perfect" and graphic screens appeared years later), he went to physics. No joke. So, what started like a joke in the math class in 6th grade, because the teacher told us a variable can be anything, etc., and it was funny, and everybody was laughing when he was writing ț^{2}+2ț+1=0 on the blackboard, ended up in changing his life forever. Last fiddled with by LaurV on 20200413 at 04:38 
20200413, 04:34  #4 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2×7×409 Posts 
https://en.wikipedia.org/wiki/Tcomma
Even a manual typewriter could do that: TBackspaceComma I don't see the problem there. It just needs a bit of engineering thinking. 
20200413, 04:44  #5 
Romulan Interpreter
Jun 2011
Thailand
21036_{8} Posts 
Oh your darkness, in spite of your avatar picture and your eternal wisdom, and you using nonJS very old stuff in your browser, you seem to be much too young to know a time when the computers didn't have a graphic screen, they even didn't use strange things called codepages, and there was no way to type on screen characters you don't have on the keyboard. And anyhow, the post says "keyboard", not "screen" or "paper". Or does your keyboard has a "ț" on it? (precious info which can be used to establish the location of the evil lair!)
Last fiddled with by LaurV on 20200413 at 04:45 
20200413, 04:57  #6  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2×7×409 Posts 
Quote:
Last fiddled with by retina on 20200413 at 04:58 

20200413, 05:42  #7 
Romulan Interpreter
Jun 2011
Thailand
8734_{10} Posts 
You ably avoided my question... Probably you have seen the Raman text, I didn't hide it well enough
Edit: Re: Typewriter. Last fiddled with by LaurV on 20200413 at 05:45 
20200413, 13:30  #8  
"Marv"
May 2009
near the Tannhäuser Gate
2^{9} Posts 
Quote:
The device on a typewriter that can move in 2 directions is a platen. Last fiddled with by tServo on 20200413 at 13:31 

20200413, 14:27  #9 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2·4,297 Posts 
When writing a report for a chemistry class I was using a Panasonic KXP1091 and was able to do that type of thing. I needed to write about sulphate and phosphate ions. I was using a simple text editor and a BASIC typesetting program. (It used slash commands inline in the text that were converted by a look up to escape codes.) I was able to produce stack subscripts and superscripts using the backspace command.
It looked more like than SO_{4}^{2} 
20200413, 17:04  #10 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2×7×409 Posts 

20200414, 12:59  #11  
Apr 2020
2 Posts 
Quote:


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