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

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.

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.

The symbol [ ] means 'the integer part of '.

Consider the three numbers

$$[2x];\ 2[x];\ [x + {1\over 2}] + [x - {1\over 2}]$$

Can they ever be equal?

Can they ever take three different values?