Everyone knows that some
right triangles have sides that are integers.
The best-known one is the 3-4-5 right triangle. There is also the 5-12-13
right triangle. In fact, there are infinitely many such triangles.
Show that any right triangle with integer sides has at least one side
that is a multiple of 3.
Hint: First show that
no number that is a perfect square has the form
3k + 2, where k is an integer.
Send your solution to sedwards@spsu.edu,
or by snail mail to Steve Edwards in the Math
Department. The names of the first solvers will be posted here.