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Hilbert's irreducibility theorem
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<p>In <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, Hilbert's irreducibility theorem, conceived by <a href="/facts/David_Hilbert/1vhlHn4b">David Hilbert</a> in 1892, states that every finite set of <a href="/facts/Irreducible_polynomial/PTeuKm4W">irreducible polynomials</a> in a finite number of variables and having <a href="/facts/Rational_number/VJQmyY05">rational number</a> coefficients admit a common specialization of a proper subset of the variables to rational numbers such that all the polynomials remain irreducible. This theorem is a prominent theorem in number theory. </p>