On some developments of the Erdős-Ginzburg-Ziv Theorem II
In this paper, we find all the solutions of the Diophantine equation in positive integer variables , where is the balancing number if the exponents , are included in the set .
In this paper, following L. Carlitz we consider some special equations of variables over the finite field of elements. We obtain explicit formulas for the number of solutions of these equations, under a certain restriction on and .