A091730 Norms of irreducible elements of Z[sqrt(-5)].

4, 5, 6, 9, 14, 21, 29, 41, 46, 49, 61, 69, 86, 89, 94, 101, 109, 121, 129, 134, 141, 149, 161, 166, 169, 181, 201, 206, 214, 229, 241, 249, 254, 269, 281, 289, 301, 309, 321, 326, 329, 334, 349, 361, 381, 389, 401, 409, 421, 446, 449, 454, 461, 469, 489

Offset: 0

Author

Paul Boddington, Feb 02 2004

Keywords

• easy
• nonn

Comments

The following lists the types of numbers which appear (p,q are distinct primes, congruences are mod 20 and the number in square brackets gives the number of irreducible elements of that norm counting a and -a only once): 4 [1]; 5 [1]; p==1,9 [2]; p^2 where p==-1,-3,-7,-9 [1]; 2p where p==3,7 [2]; p^2 where p==3,7 [3]; pq where p,q==3,7 [4].

References

• David A. Cox, Primes of the form x^2+ny^2, Wiley, 1989.
• A. Frohlich and M. J. Taylor, Algebraic number theory, Cambridge university press, 1991.