Unrolling Residues to Avoid Progressions
نویسندگان
چکیده
منابع مشابه
Unrolling residues to avoid progressions
Mathematics is often described as the study of patterns, some of the most beautiful of which are periodic. In the integers these periodic patterns take the form of arithmetic progressions, i.e., a set of integers which are equally spaced, or have the same common difference. For example, 5, 11, 17, 23, 29 is an arithmetic progression with 5 terms where consecutive terms have a difference of 6. S...
متن کاملPower Residues and Nonresidues in Arithmetic Progressions
Let A: be an integer > 2 andp a prime such that vk(p) = (k,p — 1) > 1. Let bn + c(n = 0,1,. ..;b > 2,1 < c < b, (b,p) — (c,p) = 1) be an arithmetic progression. We denote the smallest kth power nonresidue in the progression bn + c by g(p,k,b,c), the smallest quadratic residue in the progression bn + c by r2(p,b,c), and the nth smallest prime kth power nonresidue by g„(p,k), n = 0, 1, 2,_ If C(p...
متن کاملEnumerating Permutations that Avoid Three Term Arithmetic Progressions
It is proved that the number of permutations of the set {1, 2, 3, . . . , n} that avoid three term arithmetic progressions is at most (2.7) n 21 for n ≥ 11 and at each end of any such permutation, at least ⌊ 2 ⌋−6 entries have the same parity.
متن کاملArithmetic Progressions That Consist Only of Reduced Residues
This paper contains an elementary derivation of formulas for multiplicative functions of m which exactly yield the following numbers: the number of distinct arithmetic progressions of w reduced residues modulo m; the number of the same with first term n; the number of the same with mean n; the number of the same with common difference n. With m and odd w fixed, the values of the first two of th...
متن کاملUnrolling Cycles to Decide Trigger Termination
Active databases have gained a substantial interest in recent years in enforcing database integrity, however, its current implementations suffer many problems such as running into an infinite loop. While deciding termination is an undecidable task, several works have been proposed to prove termination under certain situations. However, most of these algorithms cannot conclude termination if a 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: Mathematics Magazine
سال: 2014
ISSN: 0025-570X,1930-0980
DOI: 10.4169/math.mag.87.2.83