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Norms of irreducible elements of Z[sqrt(-5)].
2

%I #6 Aug 20 2015 03:00:40

%S 4,5,6,9,14,21,29,41,46,49,61,69,86,89,94,101,109,121,129,134,141,149,

%T 161,166,169,181,201,206,214,229,241,249,254,269,281,289,301,309,321,

%U 326,329,334,349,361,381,389,401,409,421,446,449,454,461,469,489

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

%C 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].

%D David A. Cox, Primes of the form x^2+ny^2, Wiley, 1989.

%D A. Frohlich and M. J. Taylor, Algebraic number theory, Cambridge university press, 1991.

%K easy,nonn

%O 0,1

%A _Paul Boddington_, Feb 02 2004