Question

Which number is called as Ramanujan Number ?

What is it's specialty ?

Answer 1

Qᴜᴇꜱᴛɪᴏɴ :

❥ Which number is called as Ramanujan Number ?

❥ What is it's specialty ?

ᴀɴꜱᴡᴇʀ :

➛ Which number is called as Ramanujan Number ?

➟ Ramanujan replied to this saying, "No Hardy, it's a very interesting number! It's the smallest number expressible as the sum of two cubes in two different ways." 1729 is the sum of the cubes of 10 and 9. Cube of 10 is 1000 and the cube of 9 is 729.

➛ What is it's specialty ?

➟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 the sum of the cubes of 10 and 9 - cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.

Hope it helps uhh !! ♥

Answer 2

Answer:

1729 is the natural number following 1728 and preceding 1730. It is a taxicab number, and is variously known as Ramanujan's number and the Ramanujan-Hardy number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation:[1][2][3][4]

← 1728 1729 1730 →

List of numbers — Integers

← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →

Cardinal

one thousand seven hundred twenty-nine

Ordinal

1729th

(one thousand seven hundred twenty-ninth)

Factorization

7 × 13 × 19

Divisors

1, 7, 13, 19, 91, 133, 247, 1729

Greek numeral

,ΑΨΚΘ´

Roman numeral

MDCCXXIX

Binary

110110000012

Ternary

21010013

Octal

33018

Duodecimal

100112

Hexadecimal

6C116

I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "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 + 103

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):

91 = 63 + (-5)3 = 43 + 33

Numbers that are the smallest number that can be expressed as the sum of two cubes in n distinct ways[5] have been dubbed "taxicab numbers". The number was also found in one of Ramanujan's notebooks dated years before the incident, and was noted by Frénicle de Bessy in 1657. A commemorative plaque now appears at the site of the Ramanujan-Hardy incident, at 2 Colinette Road in Putney.[6]

The same expression defines 1729 as the first in the sequence of "Fermat near misses" (sequence A050794 in the OEIS) defined, in reference to Fermat's Last Theorem, as numbers of the form 1 + z3 which are also expressible as the sum of two other cubes.