Selected Topics on Polynomials

A₁ A₂ algebraic number field algebraically closed arithmetic progressions assume B₁ Bauerian C₁ condition conjugates const contradiction coprime Corollary cyclotomic polynomial deg F degree denote Diophantine equations divisor equations exist integers exist polynomials extension extra point F X1 F₁ finite follows G₁ G₂ H₂ Hence Hilbert's irreducibility theorem holds implies indeterminate coefficients inductive assumption integral polynomial integral resultant integral vector L₁ L₂ leading coefficient Lemma linear Lüroth's theorem mod char mod q monic monic polynomial monomials multilinear form Nk/k normal closure P₁ polynomial F positive integers prime ideals Proof of Theorem prove rational functions reducible respect right hand side satisfying Schinzel simple zeros solvable substitution Suppose t₁ T₂ Theorem 21 Theorem 34 variables whence x₁ Y₁ σ σ