Problem 46099. Identify full reptend primes

Created by ChrisR

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{"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>

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Problem 46099. Identify full reptend primes

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