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### Srinivasa Ramanujan

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

I would like (in terms a 12-yr-old can understand) an explanation of
the mathematical contributions of Srinivasa Ramanujan, and why they
are significant. If possible, I would also like a simple sample
"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.

Thanks,
Paul Gee
```

```
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 here's something that is fairly easy to
understand:

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(5m+4) is always divisible by 5
p(7m+5) is always divisible by 7
p(11m+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 Exponents
Middle School Exponents

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