A Kloosterman sum is defined as
$$K(a,b;m)=\sum_{\substack{ 0\leq x \leq m-1\\\gcd(x,m)=1}} e^{2\pi \mathcal{i} (ax+bx^*)/m}$$
where $a,b,m \in \mathbb{N}$ and $x^*$ is the inverse of $x$ modulo $m$.
How can I show that
$$K(1,1;16n)\neq 0$$
for odd $n$?