# Square numbers

**44**NRICH Mathematical resources connected to

**Square numbers**

problem

Favourite

### Square subtraction

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?

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### Few and far between?

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

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Favourite

### Generating Triples

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?

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### Pythagorean Quadruple

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

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### Robert's spreadsheet

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

problem

Favourite

### Light the Lights Again

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?

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### Four Coloured 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?