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which is an instance of [[Pell's equation]]. This particular equation is solved by the [[Pell number]]s {{math|''P''<sub>''k''</sub>}} as<ref>
{{cite book |last1=Hardy |first1=G. H. |authorlink1=G. H. Hardy |last2=Wright |first2=E. M. |authorlink2=E. M. Wright |title=An Introduction to the Theory of Numbers |edition=5th |year=1979 |publisher=Oxford University Press |isbn=0-19-853171-0 |page=[https://archive.org/details/introductiontoth00hard/page/210 210] |quote=Theorem 244 |url-access=registration |url=https://archive.org/details/introductiontoth00hard/page/210 }}
</ref>
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