Here is a possible way to create a simple substitution cipher. We can label letters in the

alphabet by their position $($their index$)$:

$\{A,B,C,$dots,$Y,Z\}longleftrightarrow\{0,1,2,3,$dots,$25\}$

In this setting, a Caesar cipher is given by choosing a fixed number $n$ to add to the

indices. The addition will be modulo $26$ since there are $26$ letters. What if instead we chose

a fixed number $n$ to multiply $($modulo $26)$ each of the indices by$?$

Are there any values of $n$ that won't yield a simple substitution cipher? Hint: Check

injectivity $($one$-$to$-$one$)$