منابع مشابه
Orders Modulo A Prime
In this article I develop the notion of the order of an element modulo n, and use it to prove the famous n 2 + 1 lemma as well as a generalization to arbitrary cyclotomic polynomials. References used in preparing this article are included in the last page. §1 Introduction I might as well state one of the main results of this article up front, so the following discussion seems a little more moti...
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Let Zp be the finite field of prime order p and A be a subset of Zp. We prove several sharp results about the following two basic questions: (1) When can one represent zero as a sum of distinct elements of A ? (2) When can one represent every element of Zp as a sum of distinct elements of A ?
متن کاملCongruences modulo Prime Powers
Let p be any prime, and let α and n be nonnegative integers. Let r ∈ Z and f (x) ∈ Z[x]. We establish the congruence p deg f k≡r (mod p α) n k (−1) k f k − r p α ≡ 0 mod p ∞ i=α ⌊n/p i ⌋ (motivated by a conjecture arising from algebraic topology), and obtain the following vast generalization of Lucas' theorem: If α > 1 and l, s, t are nonnegative integers with s, t < p, then 1 ⌊n/p α−1 ⌋! k≡r (...
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متن کاملOn the least prime primitive root modulo a prime
We derive a conditional formula for the natural density E(q) of prime numbers p having its least prime primitive root equal to q, and compare theoretical results with the numerical evidence. 1. Theoretical result concerning the density of primes with a given least prime primitive root Let us denote, following Elliott and Murata [4], by g(p) and G(p) the least primitive and the least prime primi...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2002
ISSN: 1071-5797
DOI: 10.1006/ffta.2001.0330