3 consecutive numbers I was playing with some numbers and just realized that:
For any 3 consecutive numbers X, Y and Z: $Y^2$ = (X*Z) + 1
For eg: Consider numbers 171, 172 and 173
$172^2$ = 29584
and 
171*173 = 29583 
Can anyone tell me if there is any proof for this and what it is known as?

Let the middle number be $x$; the other two are $x-1$ and $x+1$. Basic algebra tells us that $(x-1)(x+1)=x^2-1$, and therefore $x^2=(x-1)(x+1)+1$. (This is true even if $x$ is not an integer.)
