Arquivo da Categoria: Number Theory

The integer 17 belongs to the residue class modulo m of 24. Find m.

Publicado em 8 de Junho de 2020 por Américo Tavares

(Old) Question posted by Felipe Maia to math.stackexchange.com : The integer 17 belongs to the residue class modulo m of 24. Find m. (…) I thought of calculating m for the values ​​of the divisors of 24, that is, making … Continuar a ler →

Publicado em Math, Mathematics Stack Exchange, Number Theory | Etiquetas , , , , , | Publicar um comentário

Maximum of the produt of k positive integers, the sum of which is 100. Problem by Vishal Lama and a solution by Neil Dickson

Publicado em 31 de Dezembro de 2009 por Américo Tavares

Problem by Vishal Lama. Maximize the value of the expression , for some positive integer , where and s are all positive integers. My (corrected) guess (Ansatz). The solution to your problem seems to be satisfied by variables, such as . … Continuar a ler →

Publicado em Matemática, Math, Number Theory, Problem, Problemas, Teoria dos Números | Etiquetas , , , | Publicar um comentário

Congruences and Divisibility — A Purdue University Problem

Publicado em 24 de Abril de 2009 por Américo Tavares

pdf: ver caderno Versão portuguesa aqui PROBLEM OF THE WEEK, Problem No. 12 (Spring 2009 Series): “ Problem. For how many positive integers is not divisible by ? Justify your answer without the use of computers. ” Here is my … Continuar a ler →

Publicado em Congruences, Math, Number Theory, Problem, Purdue University | Etiquetas , | 6 Comentários

My solution to the Problem Of the Week-9 [Todd and Vishal’s blog]: Period of a decimal expansion

Publicado em 2 de Outubro de 2008 por Américo Tavares

pdf: included in Caderno (see “caderno” page) I submitted a solution to the following Problem that  was accepted. Find the length of the period of the repeating decimal representation of My Solution: The repeating decimal representation of the number is . … Continuar a ler →

Publicado em Caderno, Matemática, Math, Number Theory, Problem, Problemas, Teoria dos Números | Etiquetas , , | Publicar um comentário