ive got the answer to this question, but it took a lot of time and was very tedious. i just want to know if there is a nice quick solution so when i hand in the worksheet it doesnt look a mess.

the question is

calculate 17^-1 in Z43 (integers mod 43)

i just did multiplication tables for both and found when 43r -17s = 1 but its not a really 'nice' method. thanks for ur time