a) Find all prime numbers p,q,r satisfying 3∤p+q+r and p+q+r and pq+qr+rp+3 are both perfect squares. b) Do there exist prime numbers p,q,r such that 3∣p+q+r and p+q+r and pq+qr+rp+3 are both perfect squares? modular arithmeticnumber theoryprime numbersnumber theory proposed