What is the multiplicative inverse of 3 module 46?

Answer 1

One way to go...

We have 3b ≡ 1 mod 46, so we can make a table of b, 3b, and 3b mod 46 and see where that takes us.

b 3b 3b mod 46

0 0 0

1 3 3 <<< clearly 3b mod 46 will be 3b so long as 3b < 46

. . .

15 45 45

16 48 2 <<< the first wrap-around

17 51 5

. . .

30 90 44

31 93 1 <<< 2nd wrap-around, this is it!

Ans: The multiplicative inverse of 3 mod 46 is 31