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.
Note that: 1000 + 729 = 1728 + 1 = 1729
This 1729 is now called Ramanujan Number