The inverse of a modulo 39 is b. What is the inverse of 14a modulo 39 in terms of b? Give your answer as an expression in terms of b.

Guest May 26, 2021

#2**+1 **

The inverse of a modulo 39 is b. What is the inverse of 14a modulo 39 in terms of b? Give your answer as an expression in terms of b.

I did this a really super long way using the Euclidean algorithm and got

14a*14b=1 mod39

so the inverse of 14a is 14b (mod39)

Maybe there is an easier way. In this case trial and error would have been easier......

It is correct though 14a*14b= 196ab = 1*1 (mod39) = 1 (mod39)

Probably the fact that 39=3*13 should have been used, but I am not sure exactly how. (I have never studied modulo arithmetic formally)

Melody May 26, 2021