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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 $n$?

 Jan 23, 2021
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\((a + b)^{-1}(a^{-1} + b^{-1}) \equiv (a + b)^{-1}(a + b)(ab)^{-1}\equiv(ab)^{-1}\equiv2\pmod{n}\)

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 Jan 23, 2021

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