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Introduction. Let Z be the set of integers Here π means the complex conjugate of π. When b ≡ 0 (mod 2) and a + b ≡ 1 (mod 4) we say that π is primary. If π or −π is primary in Z[i], then we may write π = ±π 1 . . . π r , where π 1 , . . . , π r are primary primes. For α ∈ Z[i] the quartic Jacobi symbol αdoi:10.4064/aa97-4-5 fatcat:igtqzyeohfbx5bbywwtich7yle