engleski

On power values of pyramidal numbers

For m >= 3, the mth order pyramidal number is defined by x(x + 1)((m-2)x+5-m)/6. These combinatorial numbers play an important role in number theory and discrete mathematics. For m = 3 and 4, all the power values of these polynomials have been already found. In the present paper the authors deal with square values for larger m. All integer solutions of the corresponding elliptic curves are given for 3 <= m <= 100, m <> 5 (Proposition 1). The main result is the resolution, for a conjecturally infinite sequence of integers m, of the corresponding elliptic diophantine equation (Theorem 2).

pyramidal numbers; square values; elliptic curves; integer points

nije evidentirano