Question

The inverse of a modulo 39 is b. What is the inverse of 4a modulo 39 in terms of b?

Answer 1

If you're told that \(\large a^{-1} \equiv b\pmod{39}\), we see that $$\large \begin{aligned} (4a)^{-1} &\equiv 4^{-1}\cdot a^{-1}\pmod{39}\\ &\equiv 4^{-1}\cdot b\pmod{39}\end{aligned}$$To complete this problem, you just need to figure out what \(4^{-1}\pmod{39}\) is equal to; this can be done by finding a \(c\) such that \(\large 4c\equiv 1\pmod{39}\) (lucky for us, this isn't too hard to solve).

Can you take things from here? :-)

Answer 2

Thanks