Here I am trying to find the multiplicative inverse of 19 respect to 29.
19x≡1(mod29)
What I tried
29=1(19)+10 19=1(10)+9 10=1(9)+1.
From backtracking, I came up with the
1=2(29)−3(19)
However, 3 is not a multiplicative inverse of the 29. Where am I making a mistake?
I looked many answers including this answer; however, couldn't figure out my mistake.
Answer
What you have found indeed is that −3≡26 is the multiplicative inverse of 19 mod29.
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