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Register a new userAn effective analytic formula for the number of distinct irreducible factors of a polynomial
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We obtain an effective analytic formula, with explicit constants, for the number of distinct irreducible factors of a polynomial $f in mathbb{Z}[x]$. We use an explicit version of Mertens theorem for number fields to estimate a related sum over rational primes. For a given $f in mathbb{Z}[x]$, our result yields a finite list of primes that certifies the number of distinct irreducible factors of $f$.
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