optics - Is the $n$ in the single slit diffraction equation for dark fringes any integer or specifically odd integers?

The equation for angular positions of dark fringes due to single slit diffraction is $a \sin(x) = n \lambda$ correct? My question is on that $n$. I read that it takes integer values which give the order of the dark fringe. But in deriving that equation they said the path difference is given by $0.5 a \sin(x)$ and that it should equal a whole number of HALF wavelengths for there to be destructive interference resulting in a dark fringe. But if the $n$ in the final equation takes an even value, e.g 2 or 4, won't the path difference be a whole number of EVEN wavelengths instead? Causing a bright fringe?