Why is $\delta[an]=\frac 1 a \delta[n]$ in discrete time? Why is $\delta[an]=\frac 1 a \delta[n]$ in discrete time? Prove. 


Hi, I want to prove it but I don’t know on what facts to rely. In continuous time we have integral and dt in that integral that turns to be dt/a for continuous time delta function. But in discrete time, we don’t have dt. So how to prove it then?
It's actually good that you couldn't prove it because the claim is wrong. Note that in discrete time we have $\delta[n]=1$ for $n=0$ and $\delta[n]=0$ for $n\neq 0$. So if $a\neq 0$, you simply get $\delta[an]=\delta[n]$ (note that $a$ must be an integer for this to make sense). If $a=0$ then $\delta[an]=1$ (for all $n$).