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Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

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?

Challenge Level

Look at the diagram below:

Which part of the diagram represents $85^2$?

Which part represents $65^2$?

Which part represents $85^2-65^2$?

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NRICH is part of the family of activities in the Millennium Mathematics Project.

NRICH is part of the family of activities in the Millennium Mathematics Project.