Displaying similar documents to “Factoring Polynomials with Rational Coefficients.”

Some observations on the Diophantine equation f(x)f(y) = f(z)²

Yong Zhang (2016)

Colloquium Mathematicae

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Let f ∈ ℚ [X] be a polynomial without multiple roots and with deg(f) ≥ 2. We give conditions for f(X) = AX² + BX + C such that the Diophantine equation f(x)f(y) = f(z)² has infinitely many nontrivial integer solutions and prove that this equation has a rational parametric solution for infinitely many irreducible cubic polynomials. Moreover, we consider f(x)f(y) = f(z)² for quartic polynomials.

An intoduction to formal orthogonality and some of its applications.

Claude Brezinski (2002)

RACSAM

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This paper is an introduction to formal orthogonal polynomials and their application to Padé approximation, Krylov subspace methods for the solution of systems of linear equations, and convergence acceleration methods. Some more general formal orthogonal polynomials, and the concept of biorthogonality and its applications are also discussed.