Let and are conjugate complex algebraic integers which generate Lucas or Lehmer sequences. We present an algorithm to search for elements of such sequences which have no primitive divisors. We use this algorithm to prove that for all and with h, the -th element of these sequences has a primitive divisor for . In the course of proving this result, we give an improvement of a result of Stewart concerning more general sequences.
Let be a field whose characteristic is not and . We give a simple algorithm to find, given , a nontrivial solution in (if it exists) to the equation . The algorithm requires, in certain cases, the solution of a similar equation with coefficients in ; hence we obtain a recursive algorithm for solving diagonal conics over (using existing algorithms for such equations over ) and over .
We study the Ljunggren equation Y² + 1 = 2X⁴ using the "multiplication by 2" method of Chabauty.
Thomas’ conjecture is, given monic polynomials
Nous présentons un exemple de courbe elliptique définie sur ℚ de rang ≥ 22 en détaillant les méthodes qui ont permis cette découverte.
First, some classic properties of a weighted Frobenius-Perron operator on as a predual of weighted Koopman operator on will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of under certain conditions.