On two Diophantine equations of Ramanujan-Nagell type

Abstract

Abstract. In this paper, we prove two conjectures of Ulas ([21]) on two Diophantine equations of Ramanujan-Nagell type. In fact, we show that the following equationshave exactly four solutions.

On the Ramanujan-Nagell type Diophantine equation x2+Akn=B

“…For examples, one can see [1]- [18], [22]- [24]. One aspect of the study of equation (1.2) is to determine the integer solutions (x, k, n).…”

On the Ramanujan-Nagell type Diophantine equation x2+Akn=B

“…This Diophantine equation has a very rich literature. For examples, one can see [1]- [18], [22]- [24]. One aspect of the study of equation (12) is to determine the integer solutions (x, k, n).…”