Orthogonality of the Möbius function to polynomials with applications to Linear Equations in Primes over ${\mathbb{F}}_p[x]$

We prove that the Möbius function is orthogonal to polynomials over ${\mathbb{F}}_q[x]$ (up to a characteristic condition). We use this orthogonality property to count prime solutions to affine-linear equations of bounded complexity in ${\mathbb{F}}_p[x]$, with analog to a work of Green and Tao.