Problem 49733. Solve the arithmetic differential equation D(n) = n

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/problems/47843-compute-the-arithmetic-derivative-of-integers\"><w:r><w:rPr><w:u/></w:rPr><w:t>Cody Problem 47843</w:t></w:r></w:hyperlink><w:r><w:t> involved the arithmetic derivative of integers. In particular, </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=\"D(p) = 1\"/></w:customXmlPr><w:r><w:t>D(p) = 1</w:t></w:r></w:customXml><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 prime and </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=\"D(mn) = n D(m) + m D(n)\"/></w:customXmlPr><w:r><w:t>D(mn) = n D(m) + m D(n)</w:t></w:r></w:customXml><w:r><w:t>. Therefore, the arithmetic derivatives of 1, 2, 3, 4, 5, and 6 are 0, 1, 1, 4, 1, and 5, respectively. </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>One might then ask about solving arithmetic differential equations (ADEs). Because the study of differential equations often starts with solving </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=\"dy/dx = y\"/></w:customXmlPr><w:r><w:t>dy/dx = y</w:t></w:r></w:customXml><w:r><w:t>, let’s consider the analogous ADE </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=\"D(n) = n\"/></w:customXmlPr><w:r><w:t>D(n) = n</w:t></w:r></w:customXml><w:r><w:t>. The definition of the arithmetic derivative shows that no prime can solve this equation, but the sample calculations above show that the first (i.e., </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=\"m = 1\"/></w:customXmlPr><w:r><w:t>m = 1</w:t></w:r></w:customXml><w:r><w:t>) solution is 4. </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 to compute the </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=\"m\"/></w:customXmlPr><w:r><w:t>m</w:t></w:r></w:customXml><w:r><w:t>th solution to this ADE. Because the solutions become large quickly, return the </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>logarithm</w:t></w:r><w:r><w:t> of the solution. </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: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; vertical-align: baseline; "><div style="block-size: 42px; 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 21px; text-align: left; transform-origin: 384px 21px; 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/problems/47843-compute-the-arithmetic-derivative-of-integers">Cody Problem 47843</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: 182.033px 7.79167px; transform-origin: 182.033px 7.79167px; unicode-bidi: normal; "> involved the arithmetic derivative of integers. In particular, <img src="data:image/png;base64,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" alt="D(p) = 1" style="width: 61.5px; height: 18.5px;" width="61.5" 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: 7.38333px 7.79167px; transform-origin: 7.38333px 7.79167px; 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: 42.0083px 7.79167px; transform-origin: 42.0083px 7.79167px; unicode-bidi: normal; "> is prime and <img src="data:image/png;base64,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" alt="D(mn) = n D(m) + m D(n)" style="width: 162px; height: 18.5px;" width="162" 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: 296.208px 7.79167px; transform-origin: 296.208px 7.79167px; unicode-bidi: normal; ">. Therefore, the arithmetic derivatives of 1, 2, 3, 4, 5, and 6 are 0, 1, 1, 4, 1, and 5, respectively. </div><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; "><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: 382.108px 7.79167px; transform-origin: 382.108px 7.79167px; unicode-bidi: normal; ">One might then ask about solving arithmetic differential equations (ADEs). Because the study of differential equations often starts with solving <img src="data:image/png;base64,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" alt="dy/dx = y" style="width: 65px; height: 18.5px;" width="65" 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: 108.783px 7.79167px; transform-origin: 108.783px 7.79167px; unicode-bidi: normal; ">, let’s consider the analogous ADE <img src="data:image/png;base64,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" alt="D(n) = n" style="width: 60px; height: 18.5px;" width="60" 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: 153.25px 7.79167px; transform-origin: 153.25px 7.79167px; unicode-bidi: normal; ">. The definition of the arithmetic derivative shows that no prime can solve this equation, but the sample calculations above show that the first (i.e., <img src="data:image/png;base64,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" alt="m = 1" style="width: 40px; height: 18px;" width="40" 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: 45.1167px 7.79167px; transform-origin: 45.1167px 7.79167px; unicode-bidi: normal; ">) solution is 4. </div><div style="block-size: 42px; 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 21px; text-align: left; transform-origin: 384px 21px; 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: 98.6583px 7.79167px; transform-origin: 98.6583px 7.79167px; unicode-bidi: normal; ">Write a function to compute the m<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: 244.142px 7.79167px; transform-origin: 244.142px 7.79167px; unicode-bidi: normal; ">th solution to this ADE. Because the solutions become large quickly, return the <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: 28.7917px 7.79167px; transform-origin: 28.7917px 7.79167px; unicode-bidi: normal; ">logarithm<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: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; "> of the solution. </div></div></div>

Solve

Solution Stats

9 Solutions
7 Solvers

Last Solution submitted on Oct 20, 2022

Last 200 Solutions

Problem Recent Solvers7

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 49733. Solve the arithmetic differential equation D(n) = n

Solution Stats

Last 200 Solutions

Problem Recent Solvers7

Suggested Problems

More from this Author184

Problem Tags

Community Treasure Hunt

Problem 49733. Solve the arithmetic differential equation D(n) = n

Solution Stats

Last 200 Solutions

Problem Recent Solvers7

Suggested Problems

More from this Author184

Problem Tags

Community Treasure Hunt

Players