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### Sum of Two Cubes

```
Date: 01/12/2002 at 07:35:59
From: Gemm
Subject: Cube numbers

Find the smallest number that can be expressed as the sum of two cube
numbers in two different ways
```

```
Date: 01/12/2002 at 17:05:48
From: Doctor Paul
Subject: Re: Cube numbers

1729 = 1^3 + 12^3 = 9^3 + 10^3

with it. The great Indian mathematician Srinivasa Ramanujan
(1887-1920) was ill in the hospital when a friend (the great British
mathematician Godfrey Hardy) came to visit him. Hardy was well
acquainted with Ramunujan's interest in numbers, so he noted that the
number of the taxi he took to get the the hospital was rather
uninteresting. The taxi number was, of course, 1729, and Ramanujan,
though ill, immediately noted that 1729 was in fact quite interesting
since it was the smallest number that could be written as a sum of two
cubes in two different ways.

How he had discovered this is anyone's guess. Computers have since
verified that his answer was correct. Ramanujan became famous for
coming up with formulas like this one off the top of his head.

more.

- Doctor Paul, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School History/Biography
High School Number Theory

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