Could anyone please take a look at the very last expression at the very bottom of Ireland&Rosen page 214? I am refering to their A Classical Introduction to Modern Number Theory, 2nd Edition. The authors claim that the decomposition form $P^{\gamma^\prime}$ follows from Lemma8 of the same page whereas by my own calculation I thought there would be an additional multiplier $f$, ie, $f$ times the existing $\gamma^\prime$ of the text.
I have been trying to figure this out since this week... I would be very grateful if anyone could help me out. Thanks!