An arithmetic version of the crosscorrelation of two sequences is defined, generalizing Mandelbaum’s arithmetic autocorrelations. Large families of sequences are constructed with ideal (vanishing) arithmetic cross-correlations. These sequences are decimations of the 2-adic expansions of rational numbers p/q such that 2 is a primitive root modulo q.

Summary This paper reports on the formalization in Mizar system [1], [2] of ten selected problems from W. Sierpinski’s book “250 Problems Elementary Number Theory” [7] (see [6] for details this concrete dataset). article is devoted mainly to arithmetic progressions: 52, 54, 55, 56, 60, 64, 70, 71, and 73 belong chapter “Arithmetic Progressions”, problem 50 “Relatively Prime Numbers”.

Exploring further the connection between exponentiation on real closed fields and existence of an integer part modelling strong fragments arithmetic, we demonstrate that each model true arithmetic is exponential field elementarily equivalent to numbers with Peano a admits isomorphism its ordered additive multiplicative group positive elements. Under assumption Schanuel’s Conjecture, obtain stre...

We establish some inequalities comparing power means of two numbers with combinations the arithmetic and geometric means. A conjecture from [Citation1] is confirmed.

In this paper we compare the performance of several range arithmetic methods in evaluating problems in symbolicnumeric circuit analysis. Symbolic-numeric circuit analysis involves solving systems of linear equations in order to obtain the values of currents and voltages in a given circuit. Symbolic circuit expressions contain a large number of product terms and long chains of arithmetic operati...

We present a coprocessor design for fast arithmetic over large numbers of cryptographic sizes. Our design provides a efficient way to prevent side channel analysis as well as fault analysis targeting modular arithmetic with large prime or composite numbers. These two countermeasure are then suitable both for Elliptic Curve Cryptography over prime fields or RSA using CRT or not. To do so, we use...

Transversal adaptive filters for digital signal processing have traditionally been implemented into DSP processors due to their ability to perform fast floating-point arithmetic. However, with its growing die size as well as incorporating the embedded DSP block, the FPGA devices have become a serious contender in the signal processing market. Although it is not yet feasible to use floating-poin...

In this study fuzzy arithmetic is presented as a tool to tackle the prediction of the amount of barium, strontium and calcium sulfates scales in oilfield operations. Since the shape of fuzzy numbers’ membership functions is a spread representative of the whole possible values for a special model parameter, fuzzy numbers are able to consider the uncertainties in parameter determinations and thus...