Suppose that the graph of a certain function, $y=f(x)$, has the property that if it is shifted $20$ units to the right, then the resulting graph is identical to the original graph of $y=f(x)$. What is the smallest positive $a$ such that if the graph of $y=f\left(\frac x5\right)$ is shifted $a$ units to the right, then we know that the resulting graph is identical to the original graph of $y=f\left(\frac x5\right)$?

Lightning Aug 2, 2018