%0 Journal Article
%T On Polynomials Solutions of Quadratic Diophantine Equations
%A Amara Chandoul
%J Advances in Pure Mathematics
%P 155-159
%@ 2160-0384
%D 2011
%I Scientific Research Publishing
%R 10.4236/apm.2011.14028
%X Let  &lt;i&gt;P&lt;/i&gt;:=&lt;i&gt;P&lt;/i&gt;(&lt;i&gt;t&lt;/i&gt;) be a polynomial in  Z[&lt;i&gt;X&lt;/i&gt;]\{0,1} In this paper, we consider the number of polynomial solutions of Diophantine equation  &lt;i&gt;E&lt;/i&gt;:&lt;i&gt;X&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;每(&lt;i&gt;P&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;每&lt;i&gt;P&lt;/i&gt;)&lt;i&gt;Y&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;每(4&lt;i&gt;P&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;每2)&lt;i&gt;X&lt;/i&gt;+(4&lt;i&gt;P&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt;每4&lt;i&gt;P&lt;/i&gt;)&lt;i&gt;Y&lt;/i&gt;=0. We also obtain some formulas and recurrence relations on the polynomial solution  (&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;&lt;i&gt;n&lt;/i&gt;&lt;/sub&gt;,&lt;i&gt;Y&lt;/i&gt;&lt;sub&gt;&lt;i&gt;n&lt;/i&gt;&lt;/sub&gt;) of &lt;i&gt;E&lt;/i&gt;
%K Polynomial Solutions
%K Pell＊s Equation
%K Diophantine Equation
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=6310