Problem 58359. List numbers that cannot be expressed as the sum of fewer than four squares

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:r><w:t>Lagrange </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Lagrange%27s_four-square_theorem\"><w:r><w:rPr><w:u/></w:rPr><w:t>proved</w:t></w:r></w:hyperlink><w:r><w:rPr/><w:t> that all positive integers can be expressed as the sum of four squares. For example, 27 = 16 + 9 + 1 + 1. However, it can also be expressed as the sum of three squares (9 + 9 + 9). In contrast, while 47 = 36 + 9 + 1 + 1, it cannot be expressed as a sum of fewer than four squares. </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 produces the </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>th member of the sequence of numbers that cannot be expressed as the sum of fewer than four non-zero squares. </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: 114px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 57px; transform-origin: 407px 57px; 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; "><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: 31.5167px 8px; transform-origin: 31.5167px 8px; unicode-bidi: normal; "><span style="">Lagrange </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Lagrange%27s_four-square_theorem"><span style=""><span style="text-decoration-line: underline; ">proved</span></span></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: 326.733px 8px; transform-origin: 326.733px 8px; unicode-bidi: normal; "><span style=""> that all positive integers can be expressed as the sum of four squares. For example, 27 = 16 + 9 + 1 + 1. However, it can also be expressed as the sum of three squares (9 + 9 + 9). In contrast, while 47 = 36 + 9 + 1 + 1, it cannot be expressed as a sum of fewer than four squares. </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: 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: 106.442px 8px; transform-origin: 106.442px 8px; unicode-bidi: normal; "><span style="">Write a function that produces the </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</span><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: 267.592px 8px; transform-origin: 267.592px 8px; unicode-bidi: normal; "><span style="">th member of the sequence of numbers that cannot be expressed as the sum of fewer than four non-zero squares. </span></span></div></div></div>

Solve

Solution Stats

4 Solutions
4 Solvers

Last Solution submitted on Jun 06, 2023

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers4

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 58359. List numbers that cannot be expressed as the sum of fewer than four squares

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers4

Suggested Problems

More from this Author217

Problem Tags

Community Treasure Hunt

Problem 58359. List numbers that cannot be expressed as the sum of fewer than four squares

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers4

Suggested Problems

More from this Author217

Problem Tags

Community Treasure Hunt

Players