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Search: id:A091730
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| A091730 |
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Norms of irreducible elements of Z[sqrt(-5)]. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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].
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REFERENCES
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D. Cox, Primes of the form x^2+ny^2, Wiley, 1989.
A. Frohlich and M. J. Taylor, Algebraic number theory, Cambridge university press, 1991.
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CROSSREFS
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Sequence in context: A073263 A039013 A020669 this_sequence A058076 A033819 A058782
Adjacent sequences: A091727 A091728 A091729 this_sequence A091731 A091732 A091733
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Boddington (psb(AT)maths.warwick.ac.uk), Feb 02 2004
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