All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Integers and Prime Relationship (Posted on 2015-09-27) Difficulty: 3 of 5
Find all integers k such that : gcd(4*M +1, k*M+1) = 1 for every integer value of M.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Proving the previous list of integers work Comment 2 of 2 |
Perhaps I should prove that my previous answer, k = 4 +/- 2^n actually works

Well (4M + 1) is relatively prime to ((4 +/- 2^n)M + 1) if and only if it is also relatively prime to their difference, which is (+/- M*2^n)

And clearly it is.  The only prime divisors of (+/- M*2^n) are 2 and prime factors of M.  All of these leave a remainder of 1 when they divide (4M+1).  

q.e,d.

  Posted by Steve Herman on 2015-09-27 19:48:11
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information