primitive representation of integers over $\mathbb{Z}_p$

Question

In Cassel's book "Rational quadratic forms" page 235 he claims that the form $$x_1^2 + x_2^2 +5(x_3^2 + x_4^2)$$ primitively represents $3 \cdot 2^{2m}$ over $\mathbb{Z}_p$ for every prime $p$ and every integer $m\geq 0$. I believe this is due to a more general fact: let $f$ be a quadratic form in $n\geq 4$ variables and $d(f)=d$. Then $f$ primitively represents every $a\in \mathbb{Z}$ over $\mathbb{Z}_p$ for all primes $p\nmid d$. I am looking for a proof of this fact. Maybe it exists in Cassel's book but I couldn't find it.