## Monday, August 11, 2008

### Two Plus Two

We all know that two times two is equal to two plus two. (2x2 = 2+2). But there more number pairs for which the sum is equal to the product of the numbers.

Keep in mind the number pairs don't have to be the same.

What are some of the answers, or do you know a good formula for solving for the answers?

1. I can't find any other whole number sets like it except 0,0. however manipulating the formula a*b=a+b returns a=b/(b-1). therefore any number 'a' returns a value 'b' which is almost always a decimal or fraction. for example 3,3/2 or 4,4/3 or 5,5/4 and the patten continues.

2. If we are not looking for integers then this should work.
x*y = x+y
or, y = x/(x-1)
Take any value of x (x not equal to 1) and get y.

3. You two figured it out. If x+y = x*y, then y = x/(x-1). There are an infinite number of answers (pairs) to this equation.

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