A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
Take any prime number greater than 3 , square it and subtract one.
Working on the building blocks will help you to explain what is
special about your results.
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?