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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?

 

I don't understand! An explanation would really help,  I don't know where to start even.

 May 22, 2020
 #1
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hmm... Is this from aops?

 May 22, 2020

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