# Finding inverses

• July 9th 2011, 02:20 PM
scruz10
Finding inverses
Just wondering if there was a method to find inverses besides just guess and check. I need to find for Z/365Z the inverses of [53], [73], [93], and [113]
• July 9th 2011, 06:38 PM
hatsoff
Re: Finding inverses
Quote:

Originally Posted by scruz10
Just wondering if there was a method to find inverses besides just guess and check. I need to find for Z/365Z the inverses of [53], [73], [93], and [113]

Under addition we the have -[53]=[-53], and so on. Multiplication is a bit trickier. Use the Euclidean algorithm to find a,b such that 53a+365b=1. Then $[53]^{-1}=[a]$. However keep in mind that [73] is NOT an element of the multiplicative group Z/365Z (because (73,365)=73).