Problem 44849. Given a base n, find the y values less or equal than 100(without 1), such that they will never produce a periodic number if we divide any whole number between some of them

Created by Fabio Squizzato

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>A periodic number depends on the base b where we are working. So, for example the number 2/3 in decimal base is periodic(0.666666666) but if we are working in base 3, the same number can be expressed as 2/10, and the result is not periodic (0.2). By this way, it is possible to enunciate:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>In base 2 or 3, all numbers will produce periodics numbers unless the number is the base or power of the base</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>In decimal base, numbers as 2,5,8,40,50 for example will never produce periodics numbers.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>By this way, you have to find when a number in any base can produce periodics numbers or not, and then find the values less or equal than 100 that in this base will never produce a periodic number.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

5 Solutions
5 Solvers

Last Solution submitted on Aug 12, 2020

Last 200 Solutions

Problem Comments

Problem Recent Solvers5

Problem Tags

base n basic matlab binario decimal factor greatest common divisor least common multiple linear algebra periodic number primes

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 44849. Given a base n, find the y values less or equal than 100(without 1), such that they will never produce a periodic number if we divide any whole number between some of them

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers5

Suggested Problems

More from this Author1

Problem Tags

Community Treasure Hunt

Problem 44849. Given a base n, find the y values less or equal than 100(without 1), such that they will never produce a periodic number if we divide any whole number between some of them

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers5

Suggested Problems

More from this Author1

Problem Tags

Community Treasure Hunt

Players