Problem 57998. Easy Sequences 111: Repnums as Hypotenuse of Pythagorean Triangles

Created by Ramon Villamangca

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:r><w:t>The number </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>111</w:t></w:r></w:customXml><w:r><w:t> belongs to a class of numbers called </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Repunit\"><w:r><w:rPr><w:b/></w:rPr><w:t>Repunit Numbers,</w:t></w:r></w:hyperlink><w:r><w:t> in which all digits are </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>1</w:t></w:r></w:customXml><w:r><w:t>. </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>For this problem, we'll define a superset of the repunit numbers which we shall call </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>repnums</w:t></w:r><w:r><w:t>, which are composed of repeated numbers. That is, if we denote repnums by </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\text{R}(x,n)</w:t></w:r></w:customXml><w:r><w:t>, then </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x</w:t></w:r></w:customXml><w:r><w:t> is the number to be repeated and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> is the number of repetitions. Hence, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\text{R}(1,3)=111</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\text{R}(25,2)=2525</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\text{R}(123,6)=123123123123123123</w:t></w:r></w:customXml><w:r><w:t> and so on.</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>We can see from the figure below that </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\text{R}(1,3)</w:t></w:r></w:customXml><w:r><w:t> can be a hypotenuse of a right triangle with integer sides (</w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Pythagorean_triple\"><w:r><w:rPr><w:b/></w:rPr><w:t>Pythagorean Triangle</w:t></w:r></w:hyperlink><w:r><w:t>).</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> </w:t></w:r><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"123\"/><w:attr w:name=\"width\" w:val=\"254\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>In fact, this is the only Pythagorean triangle that can be formed with hypotenuse equal to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\text{R}(1,3)</w:t></w:r></w:customXml><w:r><w:t>. There is also only one Pythagorean triangle with hypotenuse equal to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\text{R}(4,5)</w:t></w:r></w:customXml><w:r><w:t>, that is the triangle with sides </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[9756,\\ 43360, \\ 44444]</w:t></w:r></w:customXml><w:r><w:t>, while there are seven Pythagorean triangles with hypotenures of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\text{R}(25,2)</w:t></w:r></w:customXml><w:r><w:t>, with legs as follows:</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> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>\\{\\ [213,\\ 2516]\\ [500,\\ 2475]\\ [707,\\ 2424]\\ [1085,\\ 2280]\\ [1173,\\ 2236]\\ [1515,\\ 2020]\\ [1680,\\ 1885]\\ \\}\n</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Create the function, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\text{C}(x,n)</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, that counts the number of Pythagorean triangles that can be formed with hypotenuse equal to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" 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<div style = "text-align: start; line-height: 20.440001px; 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: none; white-space: normal; "><div style="block-size: 435px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 217.5px; transform-origin: 407px 217.5px; vertical-align: baseline; "><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: 0px 0px; transform-origin: 0px 0px; ">The number <img src="data:image/png;base64,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" width="25.5" height="18" style="width: 25.5px; height: 18px;"><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: 0px 0px; transform-origin: 0px 0px; "> belongs to a class of numbers called <a target='_blank' href = "https://en.wikipedia.org/wiki/Repunit">Repunit Numbers,</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: 0px 0px; transform-origin: 0px 0px; "> in which all digits are 1<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: 0px 0px; transform-origin: 0px 0px; ">. </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: 0px 0px; transform-origin: 0px 0px; ">For this problem, we'll define a superset of the repunit numbers which we shall call <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: 0px 0px; transform-origin: 0px 0px; ">repnums<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: 0px 0px; transform-origin: 0px 0px; ">, which are composed of repeated numbers. That is, if we denote repnums by <img src="data:image/png;base64,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" width="46" height="19" style="width: 46px; height: 19px;"><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: 0px 0px; transform-origin: 0px 0px; ">, then x<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: 0px 0px; transform-origin: 0px 0px; "> is the number to be repeated and n<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: 0px 0px; transform-origin: 0px 0px; "> is the number of repetitions. Hence, <img src="data:image/png;base64,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" width="87" height="19" style="width: 87px; height: 19px;"><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: 0px 0px; transform-origin: 0px 0px; ">, <img 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src="data:image/png;base64,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" width="214.5" height="19" style="width: 214.5px; height: 19px;"><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: 0px 0px; transform-origin: 0px 0px; "> and so on.</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: 0px 0px; transform-origin: 0px 0px; ">We can see from the figure below that <img src="data:image/png;base64,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" width="46" height="19" style="width: 46px; height: 19px;"><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: 0px 0px; transform-origin: 0px 0px; "> can be a hypotenuse of a right triangle with integer sides (<a target='_blank' href = "https://en.wikipedia.org/wiki/Pythagorean_triple">Pythagorean Triangle</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: 0px 0px; transform-origin: 0px 0px; ">).</div><div style="block-size: 129px; 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 64.5px; text-align: left; transform-origin: 384px 64.5px; 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: 0px 0px; transform-origin: 0px 0px; "> <img class="imageNode" width="254" height="123" style="vertical-align: baseline;width: 254px;height: 123px" 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data-image-state="image-loaded"></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: 0px 0px; transform-origin: 0px 0px; ">In fact, this is the only Pythagorean triangle that can be formed with hypotenuse equal to <img src="data:image/png;base64,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" width="46" height="19" style="width: 46px; height: 19px;"><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: 0px 0px; transform-origin: 0px 0px; ">. There is also only one Pythagorean triangle with hypotenuse equal to <img src="data:image/png;base64,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" width="46" height="19" style="width: 46px; height: 19px;"><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: 0px 0px; transform-origin: 0px 0px; ">, that is the triangle with sides <img src="data:image/png;base64,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" width="140" height="19" style="width: 140px; height: 19px;"><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: 0px 0px; transform-origin: 0px 0px; ">, while there are seven Pythagorean triangles with hypotenures of <img src="data:image/png;base64,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" width="53.5" height="19" style="width: 53.5px; height: 19px;"><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: 0px 0px; transform-origin: 0px 0px; ">, with legs as follows:</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: 0px 0px; transform-origin: 0px 0px; "> <img 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" width="620.5" height="19" style="width: 620.5px; height: 19px;"></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: 0px 0px; transform-origin: 0px 0px; ">Create the function, <img src="data:image/png;base64,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" width="46" height="19" style="width: 46px; height: 19px;"><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: 0px 0px; transform-origin: 0px 0px; ">, that counts the number of Pythagorean triangles that can be formed with hypotenuse equal to <img src="data:image/png;base64,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" width="46" height="19" style="width: 46px; height: 19px;"><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: 0px 0px; transform-origin: 0px 0px; ">.</div></div></div>

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David Hill on 25 May 2023

I think test 2 might be wrong. C(1,1) should be 0, but I believe you are counting it as 1.

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Problem 57998. Easy Sequences 111: Repnums as Hypotenuse of Pythagorean Triangles

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Problem 57998. Easy Sequences 111: Repnums as Hypotenuse of Pythagorean Triangles

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