Geodesic
A Sequence of Results on Class Number Congruences
Canadian mathematical bulletin, Tome 36 (1993) no. 2, pp. 139-143

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DOI

Let p ≡ 1 mod 8 be a rational prime and let h(—p) be the class number of . In [1], Barrucand and Cohn show that h(-p) = 0 mod 8 iff p = x2 + 32y2 for some x,y € Z. In this article, we generalize their result to a family of relative quadratic extensions K/F, where Fk is the maximum totally real subfield of Q(ζ2k+2 ), and a power of a prime of Fk from a family of positive density.
DOI : 10.4153/CMB-1993-020-x
Mots-clés : 11R11 
Costa, Antone. A Sequence of Results on Class Number Congruences. Canadian mathematical bulletin, Tome 36 (1993) no. 2, pp. 139-143. doi: 10.4153/CMB-1993-020-x
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     author = {Costa, Antone},
     title = {A {Sequence} of {Results} on {Class} {Number} {Congruences}},
     journal = {Canadian mathematical bulletin},
     pages = {139--143},
     year = {1993},
     volume = {36},
     number = {2},
     doi = {10.4153/CMB-1993-020-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-020-x/}
}
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