In many NTRU material it is said that with our choice of the polynomial $f$, it will almost always have an inverse. Maybe it's a stupid question, but why will it almost always have an inverse element? And why is it recommended to take the polynomial $1 + pF$ in order to have the inverse? And one more question: why is it necessary in this scheme that $g$($x$) does not have an inverse element? What is this restriction used for?