# Egyptian fractions

Let $$P_1,P_2,P_3, \cdots P_{10}$$ be distinct primes, and let $$\displaystyle n=\prod_{i=1}^{10} P_i$$. For some $$x,y\in\mathbb{N}$$ we have

$\frac{1}{n}=\frac{1}{x}+\frac{1}{y}$

Surprisingly, the number of ordered solutions for this equation is always $$p^k$$ for a prime $$p$$ and integer $$k$$. What is $$p+k$$?

×