Part 1: Recreation of Number on 1729
Part 2: Magic Square

This paper brings representations of 1729, a famous Hardy-Ramanujan number in different situations. These representations are of crazy-type, single digit, single letter, Selfie-type, running expressions, selfie fractions, equivalent fractions, Triangular, Fibonacci, fixed digits repetitions prime numbers patterns , Pythagorean triples, palindromic-type, polygonal-type, prime numbers, embedded, repeated, etc. Ideas toward magic squares are also extended. Some quotes and historical notes on Ramanujan’s life are also specified.

This work brings magic squares connected with S. Ramanujan’s life and with Hardy-Ramanujan number 1729. There are three different types of magic squares. The first type is based on some historical years of S. Ramanujan’s life. The second type is with magic sum as 1729. In this case the magic squares constructed are of orders 7, 13, 14 and 19. The third type is magic squares based on Pythagorean tripes where the number 1729 is one the entry. In this case the magic squares constructed are of orders 6, 7, 11 and 19.

It is revised and extended version of author’s previos work. Below is a link of this work for download.

Inder J. Taneja, Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729, Zenodo, December 20, 2024, pp. 1-127, https://doi.org/10.5281/zenodo.14538297

Below are the itens that we worked with magic squares on Hardy Ramanujan Number-1729

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