Let  $A=\{k/k\in W\&\sqrt{k^2-kp}=N\}$ ; where N is  Natural number, W is a whole number  and p - odd prime number, then which of the following is/are true ?

$\sqrt{k^2-pk}=n\Rightarrow K=\frac{p\pm \sqrt{p^2+4n^2}}{2} \Rightarrow p^2+4n^2=m^2$

$$\begin{gathered} \to m-2n=1\&m+2n=p^2,n\ge 3 \\ \Rightarrow m=\frac{p^2+1}{2},n=\frac{p^2-1}{4} \\ \& k=\frac{p\pm m}{2},=\frac{2p\pm (p^2+1)}{4}\Rightarrow k=\frac{{(p+1)}^2}{4} \end{gathered}$$

(negative value is committed )