Novel Parametric Solutions for the Ideal and Non-Ideal Prouhet Tarry Escott Problem

A New Proof of the Prouhet-tarry-escott Problem

The famous Prouhet-Tarry-Escott problem seeks collections of mutually disjoint sets of non-negative integers that have equal sums of like powers. In this paper we present a new proof of the solution to this problem by deriving a generalization of the product generating function formula for the classical Prouhet-Thue-Morse sequence.

Pure product polynomials and the Prouhet-Tarry-Escott problem

An n-factor pure product is a polynomial which can be expressed in the form Qn i=1(1−xi) for some natural numbers α1, . . . , αn. We define the norm of a polynomial to be the sum of the absolute values of the coefficients. It is known that every n-factor pure product has norm at least 2n. We describe three algorithms for determining the least norm an n-factor pure product can have. We report re...

Computational investigations of the Prouhet-Tarry-Escott Problem

We describe a method for searching for ideal symmetric solutions to the Prouhet-Tarry-Escott Problem. We report results of extensive searches for solutions of sizes up to 12. We found two solutions of size 10 that are smaller by two orders of magnitude than the solution found by A. Letac in the 1940s, which was the smallest size 10 solution known before our search. 1. The Prouhet-Tarry-Escott P...

A new parametric method for ranking fuzzy numbers based on positive and negative ideal solutions

Non-ideal memristors for a non-ideal world

Memristors have pinched hysteresis loops in the V − I plane. Ideal memristors are everywhere non-linear, cross at zero and are rotationally symmetric. In this paper we extend memristor theory to produce different types of non-ideality and find that: including a background current (such as an ionic current) moves the crossing point away from zero; including a degradation resistance (that increas...