Displaying similar documents to “Polynomial squares of the form a X m + b ( 1 - X ) n + c ”

Diophantine equations with linear recurrences An overview of some recent progress

Umberto Zannier (2005)

Journal de Théorie des Nombres de Bordeaux

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We shall discuss some known problems concerning the arithmetic of linear recurrent sequences. After recalling briefly some longstanding questions and solutions concerning zeros, we shall focus on recent progress on the so-called “quotient problem” (resp. " d -th root problem"), which in short asks whether the integrality of the values of the quotient (resp. d -th root) of two (resp. one) linear recurrences implies that this quotient (resp. d -th root) is itself a recurrence. We shall also...

Comments on the height reducing property

Shigeki Akiyama, Toufik Zaimi (2013)

Open Mathematics

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A complex number α is said to satisfy the height reducing property if there is a finite subset, say F, of the ring ℤ of the rational integers such that ℤ[α] = F[α]. This property has been considered by several authors, especially in contexts related to self affine tilings and expansions of real numbers in non-integer bases. We prove that a number satisfying the height reducing property, is an algebraic number whose conjugates, over the field of the rationals, are all of modulus one,...

Solving quadratic equations over polynomial rings of characteristic two.

Jorgen Cherly, Luis Gallardo, Leonid Vaserstein, Ethel Wheland (1998)

Publicacions Matemàtiques

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We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation antn + ...+ a0 = 0 with coefficients ai in A, our problem is to find its roots in A. We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction,...