Problem 54089. Ramanujan's Number

Created by Mehmet OZC

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://en.wikipedia.org/wiki/1729_(number)\"><w:r><w:t>About 1729</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>1729 = 1^3 + 12^3=9^3+10^3</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>1729 is the first positive integer which can be expressed as the sum of two positive cubes in two different ways.</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>Calculate the second, third, fourth ... positive integers which can be expressed as the sum of two positive cubes in two different ways.</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: 20.44px; 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 solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 66px; transform-origin: 406.5px 66px; 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: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><a target='_blank' href = "https://en.wikipedia.org/wiki/1729_(number)"><span style=""><span style="">About 1729</span></span></a></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: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="169" height="19" style="width: 169px; height: 19px;"></span></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: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 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; "><span style="">1729 is the first positive integer which can be expressed as the sum of two positive cubes in two different ways.</span></span></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: 383.5px 21px; text-align: left; transform-origin: 383.5px 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; "><span style="">Calculate the second, third, fourth ... positive integers which can be expressed as the sum of two positive cubes in two different ways.</span></span></div></div></div>

Solve

Solution Stats

16 Solutions
6 Solvers

Last Solution submitted on May 21, 2022

Last 200 Solutions

Problem Recent Solvers6

Problem Tags

number ramanujan

Community Treasure Hunt

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

Start Hunting!

Problem 54089. Ramanujan's Number

Solution Stats

Last 200 Solutions

Problem Recent Solvers6

Suggested Problems

More from this Author76

Problem Tags

Community Treasure Hunt

Problem 54089. Ramanujan's Number

Solution Stats

Last 200 Solutions

Problem Recent Solvers6

Suggested Problems

More from this Author76

Problem Tags

Community Treasure Hunt

Players