Construction of a repetitive magic square with Ramanujan's number as its product

Prasantha Bharathi Dhandapani; Víctor Leiva; Carlos Martin-Barreiro

doi:10.1016/j.heliyon.2022.e12046

Construction of a repetitive magic square with Ramanujan's number as its product

Heliyon. 2022 Nov 29;9(1):e12046. doi: 10.1016/j.heliyon.2022.e12046. eCollection 2023 Jan.

Authors

Prasantha Bharathi Dhandapani¹, Víctor Leiva², Carlos Martin-Barreiro^{3

4}

Affiliations

¹ Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore, Tamil Nadu, India.
² School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile.
³ Faculty of Natural Sciences and Mathematics, Escuela Superior Politécnica del Litoral ESPOL, Guayaquil, Ecuador.
⁴ Faculty of Engineering, Universidad Espíritu Santo, Samborondón, Ecuador.

Abstract

In this article, we build a repetitive magic square by multiplying four elements. This square is a matrix with its corresponding elements. The elements of this matrix that take different values allow us to obtain Ramanujan's number 1729 as its multiplicative magic constant. The additive magic constant of the square is the number 40. The elements of these magic constants form an arithmetic progression. An algorithm to build magic squares is also proposed.

Keywords: Arithmetic progression; Diophantine equation; Latin square; Magic elements; Sequences; Square matrix.