Primey Polynomial

Algebra Level pending

There exists a quintic (\(5^\text{th} \) degree) polynomial \(f(x)\) with \(f :\mathbb N\rightarrow \mathbb N\) of with integer coefficients such that for every prime \(p\) there exists a prime \(q\) and a natural number \(r\) such that \(f(p)=q^r\).

Determine \( f(6) \).

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