# Multiplication Inverses - how to express best?

• Oct 12th 2009, 05:32 PM
dxcx2
Multiplication Inverses - how to express best?
* Looking at modular multiplication on Zn - Take the set of integers Z17 * - what are all the inverses of all elements in Z17 ?
• Oct 12th 2009, 06:38 PM
Bruno J.
Write the multiplication table to find the inverses by brute force, or use the division algorithm.
• Oct 12th 2009, 06:57 PM
dxcx2
True, both would work, can you give an example of how you would do this? I'm looking at considering different ways of expressing the answer - Thanks
• Oct 12th 2009, 08:47 PM
tonio
Quote:

Originally Posted by dxcx2
True, both would work, can you give an example of how you would do this? I'm looking at considering different ways of expressing the answer - Thanks

You can try little arithmetic tricks: the inverse of 1 is 1, the inverse of 2 is 9, the inverse of 3 is 6, the inverse of 4 = 2^2 is 4^(-1) = 2^(-2) = (2^(-1))^2 = 9^2 = 13 (everything here's done modulo 17, of course),
the inverse of 5 is 7, the inverse of 10 = 2*5 is 10^(-1) = 2^(-1)*5^(-1) = 9*7 = 12 , etc.
If your other option is write down multiplication tables I think the above can be shorter.

Tonio