Question 41
a. Find all prime triples $(p, q, r)$ such that $3 \nmid p+q+r$ and both $p+q+r$, $pq+qr+rp+3$ are perfect squares.
b. Is there any prime triple $(p, q, r)$ such that $3 \nmid p+q+r$ and both $p+q+r$, $pq+qr+rp+3$ are perfect squares.
b. Is there any prime triple $(p, q, r)$ such that $3 \nmid p+q+r$ and both $p+q+r$, $pq+qr+rp+3$ are perfect squares.