Integer between the 's p and p+2 is a perfect square. Explain why there exists...

Integer between the 's p and ${\displaystyle p+2}$ is a perfect square. Explain why there exists an integer n such that
${\displaystyle 4n^2-1=p}$
a) Is the integer between p and ${\displaystyle p+2}$ odd or even?
b) Assume additionally that the integer between the 's p and ${\displaystyle p+2}$ is a perfect square.
c) By considering ${\displaystyle (2n-1)(2n+1)}$, find the only possible value of p.