# A Complex Logic Puzzle!

Algebra Level 5

Pratik and Dhyan have the following conversation about their favorite numbers. Assuming they are both perfectly logical, which of the answer choices is equal to 1?

$$\quad$$ Pratik:
My favorite number, $$P,$$ is a perfect 6th power greater than $$1.$$

$$\quad$$ Dhyan:
My favorite number, $$D,$$ is not a real number -- but it does have the cool property that $$D^{2015}=1.$$

$$\quad$$ Pratik:
That doesn't help me much! I can think of more than $$P$$ numbers that could be your favorite.

$$\quad$$ Dhyan:
Well, then I know the value of $$D^P.$$

Note: You may find it useful to know that $$2015 = 5 \times13 \times 31.$$

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