Naslov
On power values of pyramidal numbers

Autori
Dujella, Andrej ; Gyory, Kalman ; Pinter, Akos

Izvornik
Acta Arithmetica (0065-1036) 155 (2012), 2; 217-226

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
pyramidal numbers; square values; elliptic curves; integer points

Sažetak
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).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA