Problem 53730. Easy Sequences 57: "Pretty-gorean" 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>A positive integer</w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Regular_number\"><w:r><w:t> </w:t></w:r></w:hyperlink><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 called a </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Regular_number\"><w:r><w:t>regular number, </w:t></w:r></w:hyperlink><w:r><w:t>if and only if there exist a non-negative integer </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>k</w:t></w:r></w:customXml><w:r><w:t>, such 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>x\\ |\\ 60^k</w:t></w:r></w:customXml><w:r><w:t>. For some reason, such a number is also refered to as an </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Talk%3ARegular_number#%22Ugly%22_numbers?\"><w:r><w:t>ugly number</w:t></w:r></w:hyperlink><w:r><w:t>. Below are the first few regular numbers:</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>\\{1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60...\\}</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:t>Pythagorean triangles are right triangles with all sides having integer lengths. </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>Write a program that counts all Pythagorean triangles whose areas are </w:t></w:r><w:r><w:rPr><w:b/><w:u/></w:rPr><w:t>non</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>-regular numbers and with no sides greater than a given limit </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>s</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><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>Below is the list of all Pythagorean triangles with non-regular areas and with all 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>\\le 100</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> </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>\\{\\ [7,24,25]\\ [20,21,29]\\ [21,28,35]\\ [12,35,37]\\ [14,48,50]\\\\\n\\ \\ [28,45,53]\\ [33,44,55]\\ [40,42,58]\\ [11,60,61]\\ [16,63,65]\\\\\n\\ \\ [33,56,65]\\ [39,52,65]\\ [42,56,70]\\ [48,55,73]\\ [24,70,74]\\\\\n\\ \\ [21,72,75]\\ [13,84,85]\\ [36,77,85]\\ [51,68,85]\\ [60,63,87]\\\\\n\\ \\ [39,80,89]\\ [35,84,91]\\ [57,76,95]\\ [65,72,97]\\ [28,96,100]\\ \\}</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:t>Therefore, for </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>s=100</w:t></w:r></w:customXml><w:r><w:t>, your program output should be </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>25</w:t></w:r></w:customXml><w:r><w:t>. </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: 294.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 147.25px; transform-origin: 407px 147.25px; 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; "><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: 54.5px 8px; transform-origin: 54.5px 8px; unicode-bidi: normal; ">A positive integer<a target='_blank' href = "https://en.wikipedia.org/wiki/Regular_number"> </a>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: 35.5px 8px; transform-origin: 35.5px 8px; unicode-bidi: normal; "> is called a <a target='_blank' href = "https://en.wikipedia.org/wiki/Regular_number">regular number, </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: 148px 8px; transform-origin: 148px 8px; unicode-bidi: normal; ">if and only if there exist a non-negative integer k<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: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; ">, such that <img src="data:image/png;base64,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" style="width: 49px; height: 19.5px;" width="49" height="19.5"><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: 19px 8px; transform-origin: 19px 8px; unicode-bidi: normal; ">. For some reason, such a number is also refered to as an <a target='_blank' href = "https://en.wikipedia.org/wiki/Talk%3ARegular_number#%22Ugly%22_numbers?">ugly number</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: 129px 8px; transform-origin: 129px 8px; unicode-bidi: normal; ">. Below are the first few regular numbers:</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: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 515.5px; height: 18.5px;" width="515.5" height="18.5"></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: 244.5px 8px; transform-origin: 244.5px 8px; unicode-bidi: normal; ">Pythagorean triangles are right triangles with all sides having integer lengths. <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: 109.5px 8px; transform-origin: 109.5px 8px; unicode-bidi: normal; ">Write a program that counts all Pythagorean triangles whose areas are <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: 13.5px 8px; transform-origin: 13.5px 8px; unicode-bidi: normal; ">non<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: 216.5px 8px; transform-origin: 216.5px 8px; unicode-bidi: normal; ">-regular numbers and with no sides greater than a given limit s<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: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">.</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: 267px 8px; transform-origin: 267px 8px; unicode-bidi: normal; ">Below is the list of all Pythagorean triangles with non-regular areas and with all sides <img src="data:image/png;base64,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" 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: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">:</div><div style="block-size: 102.5px; 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 51.25px; text-align: left; transform-origin: 384px 51.25px; 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: 56px 8px; transform-origin: 56px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 407px; height: 102.5px;" width="407" height="102.5"></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: 46px 8px; transform-origin: 46px 8px; unicode-bidi: normal; ">Therefore, for <img src="data:image/png;base64,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" style="width: 50px; height: 18px;" width="50" 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: 103.5px 8px; transform-origin: 103.5px 8px; unicode-bidi: normal; ">, your program output should be <img src="data:image/png;base64,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" style="width: 18px; height: 18px;" width="18" 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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; ">. </div></div></div>

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Last Solution submitted on Oct 09, 2022

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David Hill on 13 Jan 2022

I am getting different answers for 1e8 and 2^27. All of my other results match yours. I get 271357762 for 1e8 and 370497786 for 2^27. Can you check your answers again.

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Problem 53730. Easy Sequences 57: "Pretty-gorean" Triangles?

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Problem 53730. Easy Sequences 57: "Pretty-gorean" Triangles?

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