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April 1969
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7 Reads
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41 Citations
Journal of Number Theory
P. Barrucand and H. Cohn recently gave a new criterion for the divisibility by 23 of the class number of √−p (p ≡ 1 mod 23). Here a similar criterion is given for the class number of √−2p (p ≠ 2), viz., that it is divisible by 23 iff p = ± 1 mod 23 and in an integral representation −2p = u2 − 2v2 with v>0 holds v ≡ 1, −(1+22) or 1, −1 mod 23 according to p ≡ + 1 or −1 mod 23.
... We list the known results on 2-divisibility of h(−2 p). For p ≡ ± 1 mod 8, write p = u 2 − 2v 2 with u, v ∈ N and u ≡ 1 mod 4. The following results are due to Rédei [4], Reichardt [5], Hasse [6] and Leonard-Williams [7]. We refer the readers to [7]. ...
Reference:
On class numbers of pure quartic fields
April 1969
Journal of Number Theory
