## WHY DO 1729 is called as Ramanujan number?

The Hardy-Ramanujan number stems from an anecdote wherein the British mathematician GH Hardy had gone to meet S Ramanujan in hospital. Hardy said that he came in a taxi having the number ‘1729’, which the British mathematician described “as rather a dull one”.

**Why did Ramanujan find the number 1729 very interesting?**

The number 1729 seemed very interesting to Ramanujan because it is the smallest expressible number as the sum of two cubes in two several ways.

**Why is 1729 a taxicab number?**

In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Hardy–Ramanujan number, is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103.

### Can we be 1729 means?

“No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.” The two different ways are: 1729 = 13 + 123 = 93 + 10….1729 (number)

← 1728 1729 1730 → | |
---|---|

Duodecimal | 100112 |

Hexadecimal | 6C116 |

**Why 1728 is a special number?**

In mathematics 1728 is the cube of 12 and, as such, is important in the duodecimal number system, in which it is represented as “1000”. It is the number of cubic inches in a cubic foot. 1728 occurs in the algebraic formula for the j-invariant of an elliptic curve.

**Is 1729 a perfect cube?**

1729 = 13 + 123 = 93 + 10. The quotation is sometimes expressed using the term “positive cubes”, since allowing negative perfect cubes (the cube of a negative integer) gives the smallest solution as 91 (which is a divisor of 1729; 19 × 91 = 1729)….1729 (number)

← 1728 1729 1730 → | |
---|---|

Duodecimal | 100112 |

Hexadecimal | 6C116 |

## Is 0 A happy number?

The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100.

**Is 4 a sad number?**

The first few unhappy numbers are 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 16, 17, 18, 20, (OEIS A031177).