Upsetting Pitagoras

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

Euclid's Algorithm I

How can we solve equations like 13x + 29y = 42 or 2x +4y = 13 with the solutions x and y being integers? Read this article to find out.

What's a Group?

Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.

Eyes Down

Age 16 to 18 Challenge Level:

If the integer part of $x$ is $a$ then $x=a + b$ where $a$ is a whole number and $0\leq b < 1$.

Try some numerical values of $x$, evaluate the three functions and record the results. What do you notice? Can you prove that different values of $x$ will produce similar findings?