A necessary and sufficient condition for the primality of Fermat numbers
نویسندگان
چکیده
منابع مشابه
A Necessary and Sufficient Condition for the Primality of Fermat Numbers
We examine primitive roots modulo the Fermat number Fm = 22 m + 1. We show that an odd integer n 3 is a Fermat prime if and only if the set of primitive roots modulo n is equal to the set of quadratic non-residues modulo n. This result is extended to primitive roots modulo twice a Fermat number.
متن کاملA generalization of a necessary and sufficient condition for primality due to Vantieghem
We present a family of congruences which hold if and only if a natural number n is prime. 2000 Mathematics Subject Classification: 11A51, 11A07. The subject of primality testing has been in the mathematical and general news recently, with the announcement [1] that there exists a polynomial-time algorithm to determine whether an integer p is prime or not. There are older deterministic primality ...
متن کاملA Necessary and Sufficient Condition for Transcendency
As has been known for many years (see, e.g., K. Mahler, /. Reine Angew. Math., v. 166, 1932, pp. 118-150), a real or complex number f is transcendental if and only if the following condition is satisfied. To every positive number co there exists a positive integer n and an infinite sequence of distinct polynomials {p,(z)} = {pr + pr z + • • • + p z } at most of 0 1 n degree n with integral coef...
متن کاملA Necessary and Sufficient Condition for Peace∗
This paper examines the possibility for two contestants to agree on a peace settlement thereby avoiding a contest, in which each would exert a costly effort given the posterior distributions inferred from the negotiation. I find a necessary and sufficient condition of the prior distributions for there to exist a negotiation mechanism that admits a peace-ensuring perfect Bayesian equilibrium. Th...
متن کاملA New Necessary and Sufficient Condition for the Riemann Hypothesis
We give a new equivalent condition for the Riemann hypothesis consisting in an order condition for certain finite rational combinations of the values of ζ(s) at even positive integers.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 2001
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2001.134197