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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?

 May 23, 2020

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