Quicker Maths

## Ramanujan Number

Posted on May 7, 2010

When you love mathematics you can see magic in numbers. Your face gets lit up when you observe something new about a number. Something similar and very interesting happened with great Indian mathematician

Srinivasa Iyengar Ramanujan

You can see the title of this post is Ramanujan Number. You might have already guessed that he might have a stumbled up on some very interesting number with some peculiar characteristics. If you have guessed that, you are right.  Ramanujan number is 1729.

1729 is also known as the Hardy – Ramanujan number . This number is also called the Taxicab number.

Ramanujan number is so named after a famous anecdote of the British mathematician G. H. Hardy regarding a hospital visit to the Indian mathematician Srinivasa Ramanujan.

In Hardy's own words:

“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 unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two positive cubes in two different ways."

The numbers is such that,

1729 = 1^3 + 12^3 = 9^3 + 10^3

Some observations related to Ramanujan Number

1. If negative cubes are allowed, 91 is the smallest possible number with similar quality 91 = 6^3 + (?5)^3 = 4^3 + 3^3
2. Interestingly 91 is also a factor of 1729. (91x19=1729)
3. If taking “positive cubes” would not have been a condition, Ramanujan number could have been ?91, ?189, ?1729, and further negative numbers
4. 1729 is also the third Carmichael number and the first absolute Euler pseudoprime.  (If you want to know more about this numbers I can discuss it in some other post)
5. Masahiko Fujiwara showed that 1729 is one of four positive integers (with the others being 81, 1458, and the trivial case 1) which, when its digits are added together, produces a sum which, when multiplied by its reversal, yields the original number:     1 + 7 + 2 + 9 = 19;                       19 x 91 = 1729
6. Till date only 10 Taxicab numbers are known.  Subsequent Taxicab numbers are found using computers.

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1. sooooo good
U can also add his characteristics.

2. very nice.but i want some interesting topics plz send to my e-mail……..thank u

3. well written. but, it will be a complete if, more numbers are added( at least 10 numbers) .pls. send me some more numbers to my id(mkkarthik245@yahoo.com mkkarthik245@gmail.com)

4. HELLO! FREINDS
I WANT TO KNOW THE MAXIMUM RAMANUJAN NUMBERS
SENT IT ON MY ID!

6. ramanujam the great scientist

7. You can add a small history of ramanujam in the beginning.
But anyway it’s good

8. i want to know relation between ramanujam and pythagorean number

9. i need various explanation of ramanujam number.. please kindly send to my mail id

10. CAN YOU GIVE SOME DETAILED INFORMATION ABOUT IT I HAVE TO WRITE AN ARTICLE ON THIS TOPIC (ramanujan’s number)

11. i need 10 hardy ramanujan numbers and their significants

12. lovely,, so good
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14. lovely,,, so good
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15. lovely ,,, so good…..
love it

17. what are the new findings about ramanujan number

18. i want to know about all taxicab number. and please tell me the reason why ramanujan number famouse? (in detail)