Charlie chose some pairs of numbers, squared them, and added them together:

$3^2 + 3^2 = 18$

$15^2 + 6^2 = 261$

$9^2 + 21^2 = 522$

His answers were all multiples of $3$.

**Can you find some other pairs of numbers whose squares add up to a multiple of 3?**

**What is special about your pairs of numbers?**

**Can you explain why? **

Alison has also been choosing pairs of numbers, squaring them, and then adding them together.

Her answers were all multiples of 4.

**Can you find some pairs of numbers whose squares add up to a multiple of 4?**

**What is special about these pairs of numbers?**

**Can you explain why?**

**Can you find pairs of square numbers that add up to multiples of 5?**

Julia wonders if $3^{444}+4^{333}$ is a multiple of $5$.

Her calculator can't help her out.

**Can you?**