Prove that $1+x+y$ not equal to $xy$, when $x$ and $y$ are positive odd numbers I was engaging in this equation and with the help of desmos.com I noticed it is not possible. So how can we prove? In which way it is easier, should I leave $x$ or $y$ alone, or is there any method different?
First of all we can define odd numbers: 

$x=2m-1 \ \  \forall \ m \in \mathbb N \ \backslash \{0\}$ and $y=2n-1 \ \  \forall \ n \in \mathbb N \ \backslash \{0\}$

Then we have $1+x+y=x\cdot y\Rightarrow -1+2m+2n=(2m-1)(2n-1)$

$2m+2n-1=4mn-2m-2n+1$

$4m+4n=4mn+2$

$2(m+n)=2mn+1$

The LHS is always even and the RHS is always odd for all $n,m \in \mathbb N \ \backslash \{0\}$
hint

$$1+x+y=xy \implies y=\frac{x+1}{x-1}$$
$$=1+\frac{2}{x-1}$$

thus
$$(x,y)=(2,3) \text{ or } (3,2)$$