# Pen-Pineapple-Apple-Pen

Algebra Level 4

$\begin{array}{rl} P + A &= AP\\ P + N &= NP\\ AP + NP &= PNAP \end{array}$ Determine all complex solutions of the system of equations above. If your set of solutions are of the following form $$\left(P_1, A_1, N_1\right), \left(P_2, A_2, N_2\right), \dots$$, input the real value of the following sum as your answer $\sum\limits_{i=1}^{\infty} P_iP_iA_iP_i$

Clarification: The concatenation of terms indicates multiplication of variables. For instance, $$AP$$ resembles the product of $$A$$ and $$P$$.

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