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).
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.)