Problem 46099. Identify full reptend primes

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/groups/50/problems/273\"><w:r><w:t>Cody Problem 273</w:t></w:r></w:hyperlink><w:r><w:t>, which is based on </w:t></w:r><w:hyperlink w:docLocation=\"https://projecteuler.net/problem=26\"><w:r><w:t>Project Euler Problem 26</w:t></w:r></w:hyperlink><w:r><w:t>, introduced me to </w:t></w:r><w:hyperlink w:docLocation=\"https://mathworld.wolfram.com/FullReptendPrime.html\"><w:r><w:t>full reptend primes</w:t></w:r></w:hyperlink><w:r><w:t>. If </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"p\"/></w:customXmlPr><w:r><w:t>p</w:t></w:r></w:customXml><w:r><w:t> is a full reptend prime, then </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"1/p\"/></w:customXmlPr><w:r><w:t>1/p</w:t></w:r></w:customXml><w:r><w:t> has a period of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"p-1\"/></w:customXmlPr><w:r><w:t>p-1</w:t></w:r></w:customXml><w:r><w:t>. That is, the decimal expansion of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"1/p\"/></w:customXmlPr><w:r><w:t>1/p</w:t></w:r></w:customXml><w:r><w:t> has strings of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"p-1\"/></w:customXmlPr><w:r><w:t>p-1</w:t></w:r></w:customXml><w:r><w:t> digits that repeat. The first five full reptend primes are 7, 17, 19, 23, and 29. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function that determines whether the input is a full reptend prime. </w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; "><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/groups/50/problems/273">Cody Problem 273</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 61.4667px 7.8px; transform-origin: 61.4667px 7.8px; unicode-bidi: normal; ">, which is based on <a target='_blank' href = "https://projecteuler.net/problem=26">Project Euler Problem 26</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57.95px 7.8px; transform-origin: 57.95px 7.8px; unicode-bidi: normal; ">, introduced me to <a target='_blank' href = "https://mathworld.wolfram.com/FullReptendPrime.html">full reptend primes</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 7.8px; transform-origin: 9.71667px 7.8px; unicode-bidi: normal; ">. If p<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.35px 7.8px; transform-origin: 51.35px 7.8px; unicode-bidi: normal; "> is a full reptend prime, then <img src="data:image/png;base64,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" alt="1/p" style="width: 27px; height: 18.5px;" width="27" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.1833px 7.8px; transform-origin: 50.1833px 7.8px; unicode-bidi: normal; "> has a period of <img src="data:image/png;base64,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" alt="p-1" style="width: 36.5px; height: 18px;" width="36.5" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108.133px 7.8px; transform-origin: 108.133px 7.8px; unicode-bidi: normal; ">. That is, the decimal expansion of <img src="data:image/png;base64,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" alt="1/p" style="width: 27px; height: 18.5px;" width="27" height="18.5"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5px 7.8px; transform-origin: 45.5px 7.8px; unicode-bidi: normal; "> has strings of <img src="data:image/png;base64,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" alt="p-1" style="width: 36.5px; height: 18px;" width="36.5" height="18"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 71.5667px 7.8px; transform-origin: 71.5667px 7.8px; unicode-bidi: normal; "> digits that repeat. The first five full reptend primes are 7, 17, 19, 23, and 29. </div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 227.033px 7.8px; transform-origin: 227.033px 7.8px; unicode-bidi: normal; ">Write a function that determines whether the input is a full reptend prime. </div></div></div>

Solve

Solution Stats

4 Solutions
2 Solvers

Last Solution submitted on Aug 09, 2020

Last 200 Solutions

Problem Recent Solvers2

Problem Tags

number theory primes

Community Treasure Hunt

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

Start Hunting!

Problem 46099. Identify full reptend primes

Solution Stats

Last 200 Solutions

Problem Recent Solvers2

Suggested Problems

More from this Author47

Problem Tags

Community Treasure Hunt

Problem 46099. Identify full reptend primes

Solution Stats

Last 200 Solutions

Problem Recent Solvers2

Suggested Problems

More from this Author47

Problem Tags

Community Treasure Hunt

Players