The simplest possible: 1 equation, 1 unknown

Algebra Level 2

Let p be an odd prime number, and k be a positive integer.

Given that \( p^{2} + p^{1} + p^{0} + 1/k \) = \( p^{2} \times p^{1} \times p^{0} \times 1/k \), what is k?

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