UNSW School Mathematics Competition Problems 1999

Let $a, b$ be the sides and $c$ the hypotenuse of a right–angled triangle. If $a, b$ and $c$ are integers, show that

  1. at least one of $a, b$ and $c$ is divisible by $5$,
  2. if none of $a, b, c$ is divisible by $7$, then either $a + b$ or $a − b$ is divisible by $7$.