Summary: Antisimple number

\n\nThe aim of this melt down - to study Antisimple returns game and their properties. When the works were draw up on the tourney solved the business of the antiproton turns, as hale as proposed and investigated their questions on this topic. Object of inquiry - Antisimple total. We say that a natural number Antisimple if each pristine factor is include in its factorisation with exponent greater than 1. We call a positive integer order antiproton (p? N), if every prime cistron is included in its factorization with king no slight than p. We say that dickens positive integers in return Antisimple if their greatest greens divisor is the number of antiprotons. Antisimple song are a natural generalization of the chore appearing in the Belgian mathematician E. Catalan correct degrees (1844), which seek to solve the groovy mathematicians such(prenominal) as Leo Gebrakus, Frenikl de Bessie L. Euler, VA Lebesgue, T. Nagel and others . In 2003, the Romanian mathematician P. Mihailescu proven Catalans conjecture. Subject of this search is relatively new. When analyzing the sources of learning directly reference point to the problem of the antiproton rime in this conceptualisation was found cardinal - this article by Senderov, B. Frenkin Hypothesis Catalana in Quantum 4, 2007 and M2032 task of antiprotons come - twins in . Senderov from the same magazine. During work of this work call for more in-depth familiarity of the theory of numbers, which were obtained from sources such as Ore O. Invitation to number theory, IM Vinogradov fundamentals of the theory of numbers, etc.