I am very confused about how to find an inverse of a modulo m. In this case I need to find the inverse of 3 modulo 7. The book says the following:
"The Euclidean algorithm ends quickly when used to find the greatest common divisor of 3 and 7.
7 = 2 x 3 + 1
From this equation we see that
-2 x 3 + 1 x 7 = 1
This shows that -2 is an inverse of 3 modulo 7. "
I follow what the book is trying to say until it says "This shows that -2 is an inverse of 3 modulo 7." I am not sure how that shows that -2 is an inverse of 3 modulo 7.
Does anyone perhaps have a nice way to find the inverse of a modulo m?