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Displaying similar documents to “3-Selmer groups for curves y 2 = x 3 + a ”

On the basic character of residue classes.

Peter J. Hilton, Jennifer Hooper, Jean Pedersen (1989)

Publicacions Matemàtiques

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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 t ≡ -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...

Symmetry of iteration graphs

Walter Carlip, Martina Mincheva (2008)

Czechoslovak Mathematical Journal

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We examine iteration graphs of the squaring function on the rings ℤ / n ℤ when n = 2 k p , for p a Fermat prime. We describe several invariants associated to these graphs and use them to prove that the graphs are not symmetric when k = 3 and when k ≥ 5 and are symmetric when k = 4 .