Math Problems, Number Theory Problems

Problem of the Day: 1/2/13

How many rectangles have an area that is a perfect square between 1 and 100, inclusive, but have unequal but integral dimensions?

Solution to yesterday’s problem:

The difference of two squares factors out to the sum and difference of their roots, as you can see below when FOILing:

(a+b)(a-b)=a^2-ab+ab-b^2=a^2-b^2

So 2013^2-2010^2 factors to (2013+2010)(2013-2010).

Simplifying, 4023\times3. Therefore the answer is 12,069.

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