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### Simple Example of Ramanujan's Work

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Date: 03/28/99 at 18:46:23
From: Paul Gee
Subject: Srinivasa Ramanujan

I would like an explanation, in a manner that a 12 year-old can
understand, of the mathematical contributions of Srinivasa Ramanujan,
and why they are significant. If possible, I would also like a simple
to 'elliptical functions' or 'elliptic integrals', 'continued
fractions', 'infinite series' or 'hypergeometric series', and
'functional equations of the zeta function'. I do not understand these
terms, and neither does my older sister, who takes Math Analysis.
```

```
Date: 03/29/99 at 12:33:12
From: Doctor Wilkinson
Subject: Re: Srinivasa Ramanujan

This is kind of a hard question to answer, since most of Ramanujan's
work was pretty advanced. But let's look at this:

Every whole number can be written as a sum of whole numbers in various
ways.

For example:

2 = 2 + 0
= 1 + 1

3 = 3 + 0
= 2 + 1
= 1 + 1 + 1

4 = 4 + 0
= 3 + 1
= 2 + 2
= 2 + 1 + 1
= 1 + 1 + 1 + 1

The number of ways that a whole number n can be written as a sum of
whole numbers is called the number of partitions of n, and is denoted
p(n). The first few values are

p(1) = 1
p(2) = 2
p(3) = 3
p(4) = 5
P(5) = 7

Ramanujan discovered some amazing divisibility properties of p(n),
namely:

p(5n+4)  is always divisible by 5
p(7n+5)  is always divisible by 7
p(11n+6) is always divisible by 11

Ramanujan and his friend G. H. Hardy also succeeded in finding an exact
formula for the function p(n).

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