33. RAMANUJAN NUMBER
 
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Prof. G. H. Hardy Visits Ramanujan
Prof. Hardy was visiting Ramanujan who was hospitalised. Ramanujan was not cheerful. Hardy wanted to pep-up his spirits.

Ramanujan's 1000 (or more) Friends
He knew that any talk of Ramanujan's friends will cheer him up. Like you know many details about each of your friends, Ramanujan knew a lot about each of his thousand (or more) friends.

Multiple of Three Primes
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."

Sum of Two Cubes in Two Ways
But Ramanujan retorted, "No Sir! 1729 is a beautiful and interesting number! It is the smallest number that can be written as the sum of two cubes in two different ways."

Test Your Skill
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 next larger such number.

(sum of two cubes in two different ways).

You can use the table below if you need.

CUBES
NumberCube NumberCube
131 93729
238 1031000
3327 1131331
4364 1231728
53125 1332197
63216 1432744
73343 1533375
83512 1634096

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

This 1729 is now called
Ramanujan Number.

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