33. RAMANUJAN NUMBER | |||
---|---|---|---|

Home | Menu | Previous | Next |

Prof. Hardy was visiting Ramanujan who was hospitalised. Ramanujan was not cheerful. Hardy wanted to pep-up his spirits.

He knew that any talk of Ramanujan's

Hardy said, "I travelled in a car with a number plate 1729. It is a product of three primes. Otherwise there is nothing interesting about it."

But Ramanujan retorted, "No Sir! 1729 is a beautiful and interesting number!

1) Who are Ramanujan's thousand (or more) friends?

2) Can you write 1729 as the product of three primes?

3) Write 1729 as 'sum of 2 cubes in 2 different ways'?

4) Find the

(sum of two cubes in two different ways).

You can use the table below if you need.

CUBES | ||||||

Number | Cube | Number | Cube | |||

1^{3} | 1 | 9^{3} | 729 | |||

2^{3} | 8 | 10^{3} | 1000 | |||

3^{3} | 27 | 11^{3} | 1331 | |||

4^{3} | 64 | 12^{3} | 1728 | |||

5^{3} | 125 | 13^{3} | 2197 | |||

6^{3} | 216 | 14^{3} | 2744 | |||

7^{3} | 343 | 15^{3} | 3375 | |||

8^{3} | 512 | 16^{3} | 4096 |

Note that: 1000 + 729 = 1728 + 1 = 1729

This 1729 is now called