mersenneforum.org  

Go Back   mersenneforum.org > New To GIMPS? Start Here! > Homework Help

Reply
 
Thread Tools
Old 2010-02-19, 22:21   #12
Joshua2
 
Joshua2's Avatar
 
Sep 2004

10258 Posts
Default

so for my example GCD(2,5) == 1 so exists inverse. So I find ax + by = 1 or -2*2 + 1*5 = 1, and I'm not quite sure what to do. Also, how would state my question in proper math context, "x^-1 = 2 mod 5" ? Any other/better ways?
Joshua2 is offline   Reply With Quote
Old 2010-02-19, 22:59   #13
Wacky
 
Wacky's Avatar
 
Jun 2003
The Texas Hill Country

108910 Posts
Default

Quote:
Originally Posted by Joshua2 View Post
My question in proper math context, "x^-1 = 2 mod 5" ? Any other/better ways?
Josh,

I am not "mathematician", nor do I claim to be. But I have met, and held interesting discussions with, some (of the best) of them.

From a "graphic" perspective, 1/X might be preferred to x^-1. However, I would consider either equally acceptable.

In the discipline of "abstract algebra", the concept of an "inverse" belongs to "fields", which are a subset of "rings". (When you start to try to understand the distinctions, you will begin to truly enter the realm of "mathematics".)

You need to understand that "mod n" is generally used to define a congruence mapping on the integers that modifies the meaning of "=".

(At this point I hope that some of the "real" mathematicians, such as Dr. Silverman, will step in and "correct" any mis-statement that I might have made.)

Thus you look for:

2 * 3 = 6 == 1 mod 5

But, I leave it to you to research the algorithms that might assist you in finding this answer.
Wacky is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Solving for x in Phi(n, x) = 0 (mod p) carpetpool Abstract Algebra & Algebraic Number Theory 1 2017-11-04 16:53
Solving x^2 + x + 1 == 0 (mod mp) paulunderwood Miscellaneous Math 17 2016-12-31 22:11
Solving x^2==1 (mod n) paulunderwood Miscellaneous Math 2 2016-12-30 07:34
New Method for Solving Linear Systems Dubslow Miscellaneous Math 24 2012-08-24 10:46
Solving modular equivalence problems flouran Math 4 2008-12-19 17:22

All times are UTC. The time now is 03:05.

Sat Sep 26 03:05:04 UTC 2020 up 16 days, 16 mins, 0 users, load averages: 1.77, 1.74, 1.60

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, 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.