Properties of balancing, cobalancing and generalized balancing numbers∗ Page 1 Annales
Mathematicae et Informaticae 37 (2010) pp. 125–138 http://ami.ektf.hu Properties of balancing …

A positive integer n is called a balancing number if 1+...+(n− 1)=(n+ 1)+···+(n+ r) for some
positive integer r. Balancing numbers and their generalizations have been investigated by …

Given m, n [ges] 2, we prove that, for sufficiently large y, the sum 1n+···+ yn is not a product of
m consecutive integers. We also prove that for m≠ n we have 1m+···+ xm≠ 1n+···+ yn …

Introduction. In recent years the explicit computation of integer points on special models of
elliptic curves received quite a bit of attention, and many papers were published on the …

We give several effective and explicit results concerning the values of some polynomials in
binary recurrence sequences. First we provide an effective finiteness theorem for certain …

In this paper we consider Diophantine equations of the form f (x)= g (y) f(x)=g(y) where ff has
simple rational roots and gg has rational coefficients. We give strict conditions for the cases …

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The following discrete geometrical question provides a background for some classical
diophantine problems. For given positive integers m, n, can an m-dimensional and an n …

While counting lattice points in octahedra of different dimensions n and m, it is an interesting
question to ask, how many octahedra exist containing equally many such points. This gives …

j= 0 ai, jXiY j, where ai, j∈ Z and m> 0, n> 0, which is irreducible in Q [X, Y]. We recall
Runge's result [14] on Diophantine equations: if there are infinitely many (x, y)∈ Z2 such that …