## Tuesday, July 16, 2013

### Question (Updated Again!)

A student of mine presented me with the following puzzle:

What three consecutive integers will fit into the following equation for a,b, and c?

(a)(b) = a+b+c

Don't look up the answer!  Think about it for a while.

Answer after the jump.

3,4, and 5.

(3)(4) = 3+4+5

I was told that these are the only three consecutive integers that will fit (UPDATE: this is very much wrong, see the comments).

(UPDATE 2:

Thank you to Robert for presenting the way to show that these are the only two sets of solutions and shame on me for not thinking of it first:

Only Two Sets of Solutions

It's also very much accessible to any of my former intermediate algebra students.)

#### 3 comments:

1. How about -1, 0, and 1?

1. Those are the first numbers I thought about and I was certain it didn't work. I have no idea why I thought that.

You embarrassed me on my own blog. Welcome to the banned list.

2. Alas, This is what I get for using my real name on the Internet.