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MATH / 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 2pmod n. Given a+b is invertible, what is the rem…

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problem

Let nn be a positive integer greater than or equal to 33. Let a,ba,b be integers such that abab is invertible modulo nn and $(ab)^{-1}\equiv 2\pmod n$. Given a+ba+b is invertible, what is the remainder when (a+b)−1(a−1+b−1)(a+b)^{-1}(a^{-1}+b^{-1}) is divided by nn?
Plain-text mathematical notation (without MathML)
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?
Original LaTeX notation
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 $n$?

level

Level 5

type

Number Theory

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Source and history

task_id
0c44066e-6b2e-5f79-98e0-874f723d799b
task_key
number~5ftheory--test--0c44066e-6b2e-5f79-98e0-874f723d799b
task_revision_id
1
config / split
number_theory / test

Official source

initial import