  Purpose of this paper is to face up to P-spin glass and Gaussian P-spin
model, i.e. spin glasses with polynomial interactions of degree P > 2. We
consider the replica symmetry and first step of replica simmetry breaking
assumptions and we solve the models via transport equation and Guerra's
interpolating technique, showing that we reach the same results. \\ Thus, using
rigorous approaches, we recover the same expression for quenched statistical
pressure and self-consistency equation in both assumption found with other
techniques, including the well-known \textit{replica trick} technique. \\ At
the end, we show that for $P=2$ the Gaussian P-spin glass model is
intrinsecally RS.
