Huh?

Algebra Level pending

If the product of three consecutive integers is equal to the middle integer, what is the least of the three integers?

1 solution

Omkar Kulkarni
May 13, 2015

You could get the answer by the method of guessing, but here's a proof. Let the integers be $n$ , $n+1$ and $n+2$ .

So $n(n+1)(n+2)=n+1$

$n(n+1)(n+2)-(n+1)=0$

$(n+1)(n(n+2)-1)=0$

$(n+1)(n^{2}+2n-1)=0$

The equation $n^{2}+2n-1=0$ does not have integral roots.

$\therefore n+1=0\Rightarrow \boxed{n=-1}$

Ohh I thought it had to be positive

Randall Yu - 6 years ago