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Ramanujan hardy number 1729

Ramanujan Number 1729

Srinivasa Ramanujan was the renowned Indian Mathematician. Though he didn't had formal education in pure mathematics, he gave nearly 3500 results in theorems and mathematical identities. 1729 was called as Ramanujan Hardy number after an interesting incident that took place between Ramanujan and his mentor, Hardy.

Hardy was paying a visit to Ramanujan, who was ill and undergoing treatment at Putney (London). After meeting him, Hardy started the conservation with a strange remark. He told, 'I thought the number of my taxicab was 1729. It seemed to me rather a dull number and I hope it was not an unfavorable Omen!'

To which Ramanujan replied that the numbers 1 - 10000 were his "personal friends". He could effortlessly tell their factors, divisors, how the number can be split & the each part of the number can be squared/cubed, to produce interesting numbers. He further added to Hardy's comment, that 1729 is not a dull number at all. It is the smallest number expressible as the sum of two cubes in two different ways.

Ramanujan gave the two positive cubes in two different ways. They are,

13 + 123 = 1 + 1728 = 1729

93 + 103 = 729 + 1000 = 1729

Later on, numbers having similar property were all called as Ramanujan Numbers & the problem of finding such numbers came to be known as Taxi Cab(2) problem.

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