20100219, 22:21  #12 
Sep 2004
1025_{8} Posts 
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?

20100219, 22:59  #13  
Jun 2003
The Texas Hill Country
1089_{10} Posts 
Quote:
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 misstatement 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. 

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  20171104 16:53 
Solving x^2 + x + 1 == 0 (mod mp)  paulunderwood  Miscellaneous Math  17  20161231 22:11 
Solving x^2==1 (mod n)  paulunderwood  Miscellaneous Math  2  20161230 07:34 
New Method for Solving Linear Systems  Dubslow  Miscellaneous Math  24  20120824 10:46 
Solving modular equivalence problems  flouran  Math  4  20081219 17:22 