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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