this task is one from John Mason (Oxford and O.U.)

it is a great way to introduce the difference of two squares since the result just drops out

the powerpoint is here

to understand what is going on

and to test out the conjecture

students need to try some examples

firstly, they need to consider how to obtain an even number difference

then several student examples can be collected on the board

and general rules considered

be aware that some numbers have more than one representation as the difference of two squares

an initial purpose for the task might be for students to write down or recall square numbers (or they could be given a list)

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