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#49 Squares and cubes
Set by Howard Williams
Take two positive whole numbers that are both less than 20. The difference in the squares of these numbers is a perfect cube and the difference in their cubes is a perfect square. (Perfect means that the root of the square or cube is a whole number.)
What are the two numbers?
There is a number between 50 and 100 that you can multiply both these numbers by and get another pair with the same property. What is it?
What property does this number have that makes this work? How can you…
