Given $N$ magnets in a 1D line with it's position, prove that there will be $N - 1$ equilibrium points and find them.

Question

Each magnet experiences a repulsive force.

The force between a magnet and an object = ($G*m1*m2$)/$d^2$

$d$ is the distance between the magnet and the object with mass $m1$ and $m2$.

$G$ is some constant.

Equilibrium occurs when pulling force from magnets in right is equal to those in left.

I have tried binary search to find some points, but I can't prove that there are $n - 1$ equilibrium point.