Chi-squared distribution multiplied by constant

Question

I have a question regarding notation.

When $\chi^2(p)$ is the chi-squared distribution with degrees of freedom $p$, then what does it mean that
$$
X \sim k \chi^2(p),
$$
where $k$ is some constant? I mean what distribution is $k \chi^2(p)$?

Answer 1

It means $X=kY$ with $Y\sim\chi^2(p)$.