Congruences Related to the Ankeny-artin-chowla Conjecture

نویسنده

  • Takashi Agoh
چکیده

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 quadratic residues and non-residues modulo p and a special type of congruence for Bernoulli numbers.

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تاریخ انتشار 2016