How do you solve the equation $ax\equiv b \pmod m$ with the extended Euclidean algorithm?
I saw that you could solve the Diophantine equation $ax-my=b$
I've seen examples but I'm still a bit confused. (Sorry if this sounds stupid)
Asked
Active
Viewed 44 times
0
-
this is equivalent of finding the inverse of a mod m – Feb 06 '21 at 15:01
-
what you need explanation for? – Feb 06 '21 at 15:04
-
How to find the inverse – Jefferson Ji Feb 06 '21 at 15:12
-
See my answers in the linked dupes for a couple worked examples (among other methods). – Bill Dubuque Feb 06 '21 at 20:58
-
The easiest way to use the classical extended Euclidean algorithm (to get the Bezout equation hence the fraction $,x\equiv a/b)$ is this forward methoid. $,x,$ uniquely exists $\bmod m \iff\gcd(b,m)= 1\ \ $ – Bill Dubuque Feb 06 '21 at 21:47