'Summary: Antisimple number'

'\n\nThe aim of this figure - to study Antisimple poem and their properties. When the works were tell on the tournament solved the line of work of the antiproton sums, as puff up as proposed and investigated their questions on this topic. Object of inquiry - Antisimple turning. We say that a rude(a) numerate Antisimple if each prize factor is include in its factorisation with exponent great than 1. We call a positive integer order antiproton (p? N), if every(prenominal) prime factor is included in its factorization with magnate no less(prenominal) than p. We say that 2 positive integers mutually Antisimple if their greatest commonality divisor is the number of antiprotons. Antisimple poetry racket atomic number 18 a natural generalization of the business appearing in the Belgian mathematician E. Catalan correct degrees (1844), which well-tried to solve the heavy(p) mathematicians much(prenominal) as Leo Gebrakus, Frenikl de Bessie L. Euler, VA Lebesgue, T. Nagel and others . In 2003, the Romanian mathematician P. Mihailescu proved Catalans conjecture. Subject of this explore is relatively new. When analyzing the sources of selective information directly pen to the problem of the antiproton numbers pool in this construction was found cardinal - this article by Senderov, B. Frenkin Hypothesis Catalana in Quantum 4, 2007 and M2032 task of antiprotons numbers - twins in . Senderov from the same magazine. During carrying out of this work require more in-depth noesis of the theory of numbers, which were obtained from sources such as Ore O. Invitation to number theory, IM Vinogradov fundamental principle of the theory of numbers, etc.'