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CTK Exchange
neat_maths
Member since Aug-22-03
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Jan-07-06, 11:01 PM (EST) |
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"Pellian Equations"
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I understand the solutions to Pellian equations of the type x^2 - n * y^2 = c lie in continued fractions. Can anyone show me the steps to solve
x^2 - 11 * y^2 = 23
for the smallest positive integer values of x and y
or
x^2 - 11 * y^2 = -23
or
x^2 = 23 - 11 * y^2 take care
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alexb
Charter Member
1739 posts |
Jan-08-06, 12:51 PM (EST) |
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1. "RE: Pellian Equations"
In response to message #0
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>x^2 - 11 * y^2 = 23 This equation has no integer solutions, since for no x we have x2 = 2 (mod 11). >x^2 - 11 * y^2 = -23 This one does have integer solutions. The best introduction into the matter is Chapter 20 in Dorrie's 100 Great Problems of Elementary Mathematics. The use of continued fractions is based on the fact that the surds are easily representable as such. |
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