- #1

mafagafo

- 188

- 12

## Homework Statement

This is a problem I had as a margin note in an old notebook that I will recycle. I want write it using LaTeX. Problem is that I also want to write it using "proper" math notation instead of English words.

Firstly, I got this:

[tex]\textrm{Proof that }\nexists x, y \in \mathbb{N}^* | x + y + xy = 36[/tex]

Which seems to be correct. (Should 'x, y' be between parentheses?)

## Homework Equations

None.

## The Attempt at a Solution

[tex]\begin{gather}

\begin{aligned}

x + y + xy

&= x + xy + y \\

&= (x + 1) (y + 1) - 1 \\

&\therefore (x + 1) (y + 1) = 37 \\

&\therefore x = 0 \lor y = 0

\notag

\end{aligned}

\end{gather}[/tex]

Now the question: how to finish this? Obviously x = 0 or y = 0 is false as neither x nor y can be 0 as the set of all N but 0 does not include 0. How do I write this?