# On the basic character of residue classes.

Título inglés On the basic character of residue classes. Sobre el carácter básico de las clases de residuo. Hilton, Peter J. ; Hooper, Jennifer ; Pedersen, Jean Dep. Math. Sci. State Univ. New York, Binghamton (New York), Estados Unidos; Dep. Math. Univ. Utah, Salt Lake City (Utah), Estados Unidos;Dep. Math. Univ. Santa Clara California, Santa Clara (California), Estados Unidos 0214-1493 1989, 33 (2): 213-225, 6 Ref. articulo Inglés Let t, b be mutually prime positive integers. We say that the residue class t mod b is basic if there exists n such that tn ≡ -1 mod b; otherwise t is not basic. In this paper we relate the basic character of t mod b to the quadratic character of t modulo the prime factors of b. If all prime factors p of b satisfy p ≡ 3 mod 4, then t is basic mod b if t is a quadratic non-residue mod p for all such p; and t is not basic mod b if t is a quadratic residue mod p for all such p. If, for all prime factors p of b, p ≡ 1 mod 4 and t is a quadratic non-residue mod p, the situation is more complicated. We define d(p) to be the highest power of 2 dividing (p-1) and postulate that d(p) takes the same value for all prime factors p of b. The t is basic mod b. We also give an algorithm for enumerating the (prime) numbers p lying in a give residue class mod 4t and satisfying d(p) = d. In an appendix we briefly discuss the case when b is even. 120501 Teoría algebraica de números MR1030965 Zbl 0699.10009 Acceso al artículo completo