Real vs. Nominal Stochastic Discount Factor in Calvo


I have a question that I have been lingering on for two days and haven’t been able to figure it out. I will post the picture of it below. I will very much appreciate it if you can help me with the problem. Thanks in advance.

This is a first order condition that needs to evaluate to zero. P_t does not depend on the sum index. Hence, you can simply divide both sides of the equation by P_t.