Congruences of Ankeny-Artin-Chowla type for pure quartic and sectic fields
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چکیده
منابع مشابه
Congruences Related to the Ankeny-artin-chowla Conjecture
Let p be an odd prime with p ⌘ 1 (mod 4) and " = (t + upp)/2 > 1 be the fundamental unit of the real quadratic field K = Q(pp) over the rationals. The Ankeny-Artin-Chowla conjecture asserts that p u, which still remains unsolved. In this paper, we investigate various kinds of congruences equivalent to its negation p | u by making use of Dirichlet’s class number formula, the products of quadrati...
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Let p be a prime congruent to 1 modulo 4, and let t, u be rational integers such that (t + u √ p )/2 is the fundamental unit of the real quadratic field Q(√p ). The Ankeny-Artin-Chowla conjecture (AAC conjecture) asserts that p will not divide u. This is equivalent to the assertion that p will not divide B(p−1)/2, where Bn denotes the nth Bernoulli number. Although first published in 1952, this...
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Let p be a prime congruent to 1 modulo 4, and let t, u be rational integers such that (t + u √ p )/2 is the fundamental unit of the real quadratic field Q(√p ). The Ankeny-Artin-Chowla conjecture (AAC conjecture) asserts that p will not divide u. This is equivalent to the assertion that p will not divide B(p−1)/2, where Bn denotes the nth Bernoulli number. Although first published in 1952, this...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1987
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000002695