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) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.

Challenge Level

A $2$-digit number is squared. When the $2$-digit number is reversed and squared, the difference between the squares is also a square.

What is the $2$-digit number?

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