Square numbers

How many triangles have all three angles perfect squares (in degrees)?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

Which numbers can we write as a sum of square numbers?

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

The sum of three square numbers equals $121$. What can those numbers be...

How many numbers do you need to remove to avoid making a perfect square?

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?