Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2
How many right-angled triangles are there with sides that are all
integers less than 100 units?
A man paved a square courtyard and then decided that it was too
small. He took up the tiles, bought 100 more and used them to pave
another square courtyard. How many tiles did he use altogether?
Published December 1997,April 1997,December 2011,February 2011.
This is the second of the two articles on right-angled triangles whose edge lengths are whole numbers. We suppose that the lengths of the two sides of a right-angled triangles are $a$ and $b$, and that the hypotenuse has length $c$ so that, by Pythagoras' Theorem,$$a^2 + b^2 = c^2$$.
In the first article we discussed the possibility of enlarging or shrinking a right-angled triangle to get another right-angled triangle whose sides also have lengths that are whole numbers, and we claimed there that apart from a possible scaling of the triangle, every such right-angled triangle has edge lengths of the form