Copyright © University of Cambridge. All rights reserved.
How many of the numbers from $1$ to $20$ can you express as the difference of two perfect squares?
What do you notice about the difference between squares of consecutive numbers?
What about the difference when I square two numbers which differ by $2$? By $3$? By $4$...?
When is the difference between two square numbers odd?
And when is it even?
What do you notice about the numbers you CANNOT make?