Complex sentence: It may however be that it applies (for some prime number) to the polynomial obtained after substitution (for some integer) of for; the fact that the polynomial after substitution is irreducible then allows concluding that the original polynomial is as well.
Split into simpler sentences: It may however be that it applies (for some prime number) to the polynomial obtained after substitution (for some integer) of for. The fact that the polynomial after substitution is irreducible then allows concluding that the original polynomial is as well.