# 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 \(2015 = 5 \times13 \times 31.\)

**Your answer seems reasonable.**Find out if you're right!

**That seems reasonable.**Find out if you're right!

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