Arithmetic Progressions with Restricted Digits
نویسندگان
چکیده
منابع مشابه
On Restricted Arithmetic Progressions over Finite Fields
Let A be a subset of Fp , the n-dimensional linear space over the prime field Fp of size at least δN (N = p), and let Sv = P −1(v) be the level set of a homogeneous polynomial map P : Fp → Fp of degree d, for v ∈ Fp . We show, that under appropriate conditions, the set A contains at least cN |S| arithmetic progressions of length l ≤ d with common difference in Sv, where c is a positive constant...
متن کاملOn Arithmetic Progressions of Integers with a Distinct Sum of Digits
Let b ≥ 2 be a fixed integer. Let sb(n) denote the sum of digits of the nonnegative integer n in the base-b representation. Further let q be a positive integer. In this paper we study the length k of arithmetic progressions n, n+ q, . . . , n+ q(k − 1) such that sb(n), sb(n+ q), . . . , sb(n+ q(k − 1)) are (pairwise) distinct. More specifically, let Lb,q denote the supremum of k as n varies in ...
متن کاملArithmetic progressions with constant weight
Let k ≤ n be two positive integers, and let F be a field with characteristic p. A sequence f : {1, . . . , n} → F is called k-constant, if the sum of the values of f is the same for every arithmetic progression of length k in {1, . . . , n}. Let V (n, k, F ) be the vector space of all kconstant sequences. The constant sequence is, trivially, k-constant, and thus dim V (n, k, F ) ≥ 1. Let m(k, F...
متن کاملArithmetic Progressions with Square Entries
We study properties of arithmetic progressions consisting of three squares; in particular, how one arithmetic progression generates infinitely many others, by means of explicit formulas as well as a matrix method. This suggests an equivalence relation could be defined on the arithmetic progressions, which lead to interesting problems for further study. The purpose of this paper is to investigat...
متن کاملArithmetic with Signed Analog Digits
This paper presents mathematical foundtions of the Overlap Resolution Number System (ORNS) which employs signed Continuous Valued Digits (CVD’s). ORNS is a redundant Number System employing residue arithmetic. In contrast to the implementation of arithmetic by binary or multiple-valued logic circuits, arithmetic operations in this novel number system are performed by analog digit manipulation c...
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: The American Mathematical Monthly
سال: 2020
ISSN: 0002-9890,1930-0972
DOI: 10.1080/00029890.2020.1682888