Freeflows
Inverse Modular Equation
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 $?
- 1
- 2
- 3
- +
- 4
- 5
- 6
- -
- 7
- 8
- 9
- $\frac{a}{b}$
- .
- 0
- =
- %
- $a^n$
- $a^{\circ}$
- $a_n$
- $\sqrt{}$
- $\sqrt[n]{}$
- $\pi$
- $\ln{}$
- $\log$
- $\theta$
- $\sin{}$
- $\cos{}$
- $\tan{}$
- $($
- $)$
- $[$
- $]$
- $\cap$
- $\cup$
- $,$
- $\infty$