# Thread: number theory algebra help

1. ## number theory algebra help

For any a, b , $\in R$ let a * b denote ab + a + b.
Show that if a* b = -1 then either a = -1 or b = -11.

Am not sure where to start, from here.

2. ## Re: number theory algebra help

I assume that R means $\mathbb{R}$, the set of real numbers.

(If R stands for a generic ring, you'll need to specify that it's a domain.)

I also assume that your "b = -11" is a typo - that you intended "b = -1"

a*b = -1 implies ab + a + b = -1.

Now write that as "a, b stuff" = 0, and it will actually factor, and from there lead you to your result.

3. ## Re: number theory algebra help

Hint: $ab + a + b + 1 = (a+1)(b+1)$.

4. ## Re: number theory algebra help

Yes thank you, it was a typo b=-1 not 11