Question

A paragraph on Hardy Ramanujan Number

Answer 1

Answer:

1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. ... 1729 is also the sum of the cubes of 12 and 1- cube of 12 is 1728 and cube of 1 is 1; adding the two results in 1729.

Answer 2

Explanation:

$\huge\star\underline\mathfrak\green{ANSWER}$

The smallest nontrivial taxicab number, i.e., the smallest number representable in two ways as a sum of two cubes. It is given by

1729=1^3+12^3=9^3+10^3.

The number derives its name from the following story G. H. Hardy told about Ramanujan. "Once, in the taxi from London, Hardy noticed its number, 1729. He must have thought about it a little because he entered the room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared, 'rather a dull number,' adding that he hoped that wasn't a bad omen. 'No, Hardy,' said Ramanujan, 'it is a very interesting number. It is the smallest number expressible as the sum of two [positive] cubes in two different ways' " (Hofstadter 1989; Kanigel 1991; Snow 1993; Hardy 1999, pp. 13 and 68).