# Arquivo de etiquetas: Problem

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

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

## My Solution of The Purdue University Problem Of The Week No. 12

My solution of POW12 was accepted. [Remark of December 19, 2009: it is only stated that it was “completely or partially proved”] (Tradução aqui) “ Problem. Find, with proof, the maximum value of where and is variable. In particular, your … Continuar a ler

Publicado em Calculus, Cálculo, Matemática, Math, Problem, Problemas, Purdue University | Etiquetas , | Publicar um comentário

## Soma telescópica. A Mathematical Reflections Undergraduate Problem. A Telescoping Sum

Here is the solution to the U115 Mathematical Reflections Problem I submitted a few months ago.

Publicado em Matemática, Math, Mathematical Reflections, Problem, Problemas | Etiquetas , , , | Publicar um comentário

## Problema do mês :: Problem of the month #1. (Valoração p-ádica :: p-adic valuation). Resolução :: Solution

ver/see Problema do mês Problem of the month Problem: Let be the greatest positive integer such that Find with proof an upper bound for Claim: is an upper bound for . Find a smaller one. Problema: Seja o maior inteiro positivo … Continuar a ler

Publicado em Matemática, Math, Problem Of The Month, Problema do mês, Problemas | | Publicar um comentário

## A mortgage problem (Problema sobre o prazo de amortização de uma hipoteca)

In  a recent post  Professor Gowers  writes on the new proposal for the A-level exam on the “Use of Mathematics”.  In it  he discusses the following discrete problem which he approaches in a way that uses  continuous techniques. ” Suppose for simplicity that the … Continuar a ler

Publicado em Cálculo financeiro, Matemática, Math, Problem, Problemas | Etiquetas , , , | Publicar um comentário

## Problema do mês :: Problem of the month #1

ver/see Problema do mês Problem of the month Resolução :: Solution Enunciado do Problema   Seja o maior inteiro positivo tal que   Determine, justificando, um majorante de Nota: não  se permite a utilização de calculadoras ou computadores. Sairá vencedora  a melhor estimativa  justificada.  Afirmação … Continuar a ler

Publicado em Matemática, Math, Problem, Problem Of The Month, Problema do mês | | 7 Comentários

## Congruences and Divisibility — A Purdue University Problem

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

## Apéry Numbers

This is a translation of a previous Portuguese post of mine.  Show that for all integers the following identity holds   Solution In order to have a short notation and because these numbers are the Apéry Numbers, let´s denote  … Continuar a ler

Publicado em Demonstração, Matemática, Math, Problem, Proof | Etiquetas , , | Publicar um comentário

## Putnam problem of the day (by the HMD dated March 1, 2008)

pdf: included in Caderno (see “caderno” page)  On March 1st, 2008, the Putnam problem of the day displayed on the  Harvard’s Math Department site was stated as follows: ” Evaluate Express your answer in the form , where are integers. “  Solution … Continuar a ler

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