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 2010-02-19, 22:21 #12 Joshua2     Sep 2004 10258 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?
2010-02-19, 22:59   #13
Wacky

Jun 2003
The Texas Hill Country

108910 Posts

Quote:
 Originally Posted by Joshua2 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.

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