Let
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
be the product of two consecutive integers greater than 2. Show that there are no integers
![x_1, x_2, \ldots, x_p](/media/m/e/3/2/e323b87f864ce273ffbf2a25b2580b9a.png)
satisfying the equation
OR
Show that there are only two values of
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
for which there are integers
![x_1, x_2, \ldots, x_p](/media/m/e/3/2/e323b87f864ce273ffbf2a25b2580b9a.png)
satisfying
%V0
Let $p$ be the product of two consecutive integers greater than 2. Show that there are no integers $x_1, x_2, \ldots, x_p$ satisfying the equation
$$\sum^p_{i = 1} x^2_i - \frac {4}{4 \cdot p + 1} \left( \sum^p_{i = 1} x_i \right)^2 = 1$$
OR
Show that there are only two values of $p$ for which there are integers $x_1, x_2, \ldots, x_p$ satisfying
$$\sum^p_{i = 1} x^2_i - \frac {4}{4 \cdot p + 1} \left( \sum^p_{i = 1} x_i \right)^2 = 1$$