  We extend Salem's Integral equation to the non-homogenous form, and offer the
associated criteria for the Riemann Hypothesis. Explicit solutions for the
non-homogenous case are given, which in turn give further insight into Salem's
criteria for the RH. As a conclusion, we show these results follow from a
corollary relating the uniqueness of solutions of the non-homogenous form with
Wiener's theorem.
