Problem 55340. Solutions to Generalized Pell Equation or Quadratic Diophantine

Created by David Hill

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<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>

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Problem 55340. Solutions to Generalized Pell Equation or Quadratic Diophantine

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Problem 55340. Solutions to Generalized Pell Equation or Quadratic Diophantine

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Last 200 Solutions

Problem Recent Solvers1

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