Pythagorean Palindrome

Algebra Level 4

Consider integers aa and PP that satisfy the equations

{(4a+5)2=a2+[4(a+1)]2P=(271a)2+[1084(a+1)]2 \begin{cases} (4a+5)^2 = a^2 + [4(a+1)]^2 \\ P =(271a)^2 + [1084(a+1)]^2\\ \end{cases}

Find sum of all value(s) of PP.

Image Credit: Wikimedia Pythagoras Theorem Proof
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