# Thread: [SOLVED] x^2 - y^2 = 1001 ; y&gt;0 , Sigma(x)=?

1. ## [SOLVED] x^2 - y^2 = 1001 ; y&gt;0 , Sigma(x)=?

What is the sum of all positive integers $x$ for which there exists a positive integer $y$ with $x^2 - y^2 = 1001$?
I (thought I) found all x:
$45^2-32^2 \leftarrow \text{ from } (7*11)*13$
$51^2-40^2 \leftarrow \text{ from } (7*13)*11$
$75^2-68^2 \leftarrow \text{ from } 7*(11*13)$

$45+51+75=171$, which is "wrong".
I think not, but is there any other $x$ for above equation?

2. Originally Posted by courteous
I (thought I) found all x:
$45^2-32^2 \leftarrow \text{ from } (7*11)*13$
$51^2-40^2 \leftarrow \text{ from } (7*13)*11$
$75^2-68^2 \leftarrow \text{ from } 7*(11*13)$

$45+51+75=171$, which is "wrong".
I think not, but is there any other $x$ for above equation?
Hint: 7 * 11 * 13 = 1 * (7 * 11 * 13)

3. ## An awkward solution.

Indeed. I would never on earth thought of that. Thank you.