talented young mathematician

2011-10-16T17:49:00.000-07:00

To expand:

First find all possible z where:

Such that:

Then:

It is important to note that the number of possible z is equal to:

Although this seems like a dauntingly large number, one can increase the efficiency of the algorithm by only "caring" about distinct coefficients.

The absolute worst case scenario is only that the number of distinct coefficients is equal to the number of partitions of n, denoted p(n), which is approximately:

*it is assumed that all variables are positive integers.

Sam Korsky, 14 years old, Northbrook, IL, USA

A formula for pi

2011-08-19T13:24:00.000-07:00

I have derived a new formula for pi, and I wanted your input on it.

Sam Korsky, 14 years old, Northbrook, IL, USA

A primality test

2011-08-19T13:23:00.003-07:00

Here's a way to test if a number is prime. What do you think?

Sam Korsky, 14 years old, Northbrook, IL, USA

A complex square

2011-08-19T13:23:00.001-07:00

Similar to this previous problem, how can we describe, using an equation, the set of all complex numbers such that if you connect the origin to , then to the point (where ), then to , then finally back to the origin, you get a square?

Eugene Bulkin, 17 years old, USA

A complex rhombus

2011-08-11T17:55:00.000-07:00

How can we describe, using an equation, the set of all complex numbers such that if you connect the origin to , then to the point (where ), then to , then finally back to the origin, you get a rhombus?

Rick Presman, 18 years old, USA