This should be easy, but I am being stupid I think.
- I have a finite field with 269 fields.
- I want to find the multiplicative inverse of 98.
- I multiply 98 by every field in the finite field (modulo 269) until the answer is 1.
- This gives me 140.
- (98 * 140) modulo 269 = 1
However, I thought I could use the multiplicative inverse instead of division? For example, instead of dividing a number by 98 (modulo 269) I could multiply it by 140 (modulo 269). This doesn't seem to be working.
Am I doing something stupid?
Any help appreciated.
[One more question if anyone can help! If the numbers I am dealing with are polynomials, can I use the same system as above, except use polynomial multiplication instead of natural number multiplication? Thanks!]