### 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.

### Always Perfect

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

# Eyes Down

##### Age 16 to 18Challenge Level

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?