= Ramanujan's Taxi Cab Numbers =

There is a well known anecdote concerning the self-taught Indian mathematical genius [[http://en.wikipedia.org/wiki/Srinivasa_Ramanujan|Srinivasa Ramanujan]]. The British mathemetician G.H. Hardy went to visit him in hospital one day, and remarked that he had travelled in taxi cab number 1729, which seemed rather a dull number. Ramanujan replied "No, Hardy! No, Hardy! It is a very interesting number. It is the smallest number expressible as the sum of two cubes in two different ways"

It's certainly true that 1729 = 1^3^ + 12^3^ = 9^3^ + 10^3^. Such numbers have become known as 'taxi cab' numbers.

Can you write an APL function which returns all the taxi cab numbers with terms up to N^3^ (where N is an integer > 0), and also displays the pairs of cubes ?

While you're at it, you might want to use APL to verify some other interesting facts about the number [[http://en.wikipedia.org/wiki/1729_(number)|1729]]. For example:

(a) In base 10 the number 1729 is evenly divisible by the sum of its digits. The same is true in base 8 and base 16, but not base 2.

(b) When the digits of 1729 are added together they produce a sum which, when multiplied by its reversal, yields the original number:

        1 + 7 + 2 + 9 = 19      ;    19 × 91 = 1729 

Can you find any other numbers which have this property?

>> [[TaxiCabNumbers/Solution|The Solution]]

 
 

Author: SimonMarsden
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CategoryPuzzles