Let n be a positive integer and a, b be invertible integers modulo n such that \(a\equiv b^{-1}\pmod n\). What is the remainder when ab is divided by n?
\(a\equiv b^{-1}\pmod n\\ a\cdot b\equiv b^{-1}\cdot b \pmod n\\ ab \equiv 1 \pmod n\)
The required remainder is 1.
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