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Simplify the equation and try to show that the equation only satisfies when $p=q=r$.
Find the sum of all $(p,q,r)$ where $p,q,r$ are nonnegative integers and $pq+qr+pr+2-(p+q+r)=pqr$.
Simplify the equation and try to show that the equation only satisfies when $p=q=r$.