Problem 55340. Solutions to Generalized Pell Equation or Quadratic Diophantine

Created by David Hill

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 generalized Pell equation is of the form: </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^2-Dy^2 = \\pm N</w:t></w:r></w:customXml><w:r><w:t>. Given D and N as inputs, output the first 50 positive integer solutions [x, y] sorted by x (smallest to largest). Both outputs should be a cell array of character arrays containing the integer solutions.</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: 63px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 31.5px; transform-origin: 407px 31.5px; vertical-align: baseline; "><div style="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; "><span style="">The generalized Pell equation is of the form: </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="98" height="19" style="width: 98px; height: 19px;"></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: 0px 0px; transform-origin: 0px 0px; "><span style="">. Given D and N as inputs, output the first 50 positive integer solutions [x, y] sorted by x (smallest to largest). Both outputs should be a cell array of character arrays containing the integer solutions.</span></span></div></div></div>

Solve

Solution Stats

1 Solutions
1 Solvers

Last Solution submitted on Aug 22, 2022

Last 200 Solutions

Problem Recent Solvers1

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 55340. Solutions to Generalized Pell Equation or Quadratic Diophantine

Solution Stats

Last 200 Solutions

Problem Recent Solvers1

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Problem 55340. Solutions to Generalized Pell Equation or Quadratic Diophantine

Solution Stats

Last 200 Solutions

Problem Recent Solvers1

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Players

WeChat