|
|||||
|
|
Combinatorially fruitful properties of 3⋅2 and 3⋅2 modulo p |
|
| Authors: | Ian Anderson |
| Institution: | a Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW, UK b School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK c Institute of Mathematics, Statistics and Actuarial Science, Cornwallis Building, University of Kent, Canterbury, Kent CT2 7NF, UK |
| Abstract: | Write a≡3⋅2−1 and  where p is an odd prime. Let c be a value that is congruent (modp) to either a or b. For any x from Zp?{0}, evaluate each of x and  within the interval (0,p). Then consider the quantity  where the differences are evaluated  in the interval (0,p−1), and the quantity  where the differences are evaluated (modp+1) in the interval (0,p+1). As x varies over Zp?{0}, the values of each of  and  give exactly two occurrences of nearly every member of 1,2,…,(p−1)/2. This fact enables a and b to be used in constructing some terraces for Zp−1 and Zp+1 from segments of elements that are themselves initially evaluated in Zp. |
| Keywords: | 2-sequencings Number theory Power-sequence terraces Prime numbers Reduced and raised differences |
| 本文献已被 ScienceDirect 等数据库收录！ | |