Pythagoras mod 5

Prove that for every right angled triangle which has sides with integer lengths: (1) the area of the triangle is even and (2) the length of one of the sides is divisible by 5.

Problem

Prove that for every right angled triangle which has sides with integer lengths:

  1. the area of the triangle is even and
  2. the length of one of the sides is divisible by 5.