find a pair of numbers who's sums are equal to their product?

Question

example 2x2=4 2+2=4

Answer 1

The trivial solution of (0,0) works.

There are lots of other solutions involving fractions. For just integers, it's a bit tougher.

x + y = x * y

If you plug in x = 3, then y = 3/2
You'll see the pattern goes on for (4, 4/3), (5, 5/4), and so on, but I don't think it becomes an integer again.

Answer 2

Yours is the only combination that works. You want to prove a + b = ab.

Case 1) Let's assume that a = b. That means a+b = 2a. So 2a = ab, so b =2. Then so does a. That's the only answer for this case.

Case 2) Let's assume a>b, and that the difference (a-b) = x. So you want to prove (b+x) + b = (b+x) * b.
Or 2b + x = b^2 + bx. b^2 will always be greater than 2b for any b>2, and bx will always be greater than x. That means the right side will always be greater than the left side, so it doesn't work.

Answer 3

2. That's the only time you'll find it. Anything below it, sum > product. Any number above 2 the product > sum.

Oh, forgot about 0,0. 0's a tricky little anomaly.

Answer 4

that 1 and zero.lol easy

Answer 5

1,2,and there's more