Notes on efficient computation of Ramanujan cubic equations
- 14 June 2022
- journal article
- research article
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Notes on Number Theory and Discrete Mathematics
- Vol. 28 (2), 350-375
- https://doi.org/10.7546/nntdm.2022.28.2.350-375
Abstract
This paper considers properties of a theorem of Ramanujan to develop properties and algorithms related to cubic equations. The Ramanujan cubics are related to the Cardano cubics and Padovan recurrence relations. These generate cubic identities related to heptagonal triangles and third order recurrence relations, as well as an algorithm for finding the real root of the relevant Ramanujan cubic equation. The algorithm is applied to, and analyzed for, some of the earlier examples in the paper.Keywords
This publication has 2 references indexed in Scilit:
- On Ramanujan type identities and Cardano formulaNotes on Number Theory and Discrete Mathematics, 2021
- Finite trigonometric sums and class numbersMathematische Annalen, 2004