Let n be a positive integer greater than or equal to 3 . Let a,b be integers such that ab is invertible modulo n and \((ab)^{-1}\equiv 2\pmod n\). Given a+b is invertible, what is the remainder when \((a+b)^{-1}(a^{-1}+b^{-1})\) is divided by n?
\((a+b)^{-1}(a^{-1}+b^{-1})=\frac{1}{ab} \)
the question has already told you that the remainder will be 2 when it is divided by n.
That is what mod means
mod means remainder.
