Nový pohled na algoritmickou matematiku
For every finite Abelian group Γ and for all , if there exists a solution of the equation in non-negative integers , where are positive integers, then the number of such solutions is estimated from below in the best possible way.
Let F(X,Y) be an irreducible binary cubic form with integer coefficients and positive discriminant D. Let k be a positive integer satisfying . We give improved upper bounds for the number of primitive solutions of the Thue inequality .
MSC 2010: 11B83, 05A19, 33C45This paper is dealing with the Hankel determinants of the special number sequences given in an integral form. We show that these sequences satisfy a generalized convolution property and the Hankel determinants have the generalized Somos-4 property. Here, we recognize well known number sequences such as: the Fibonacci, Catalan, Motzkin and SchrÄoder sequences, like special cases.