Quadratic ideals, indefinite quadratic forms and some specific diophantine equations - Ahmet Tekcan; Seyma Kutlu (Boletim da Sociedade Paranaense de Matemática, 2018)
Let $k≥ 1$ be an integer and let $P=k+2,Q=k$ and $D=k^{2}+4$. In this paper, we derived some algebraic properties of quadratic ideals $I_{γ}$ and indefinite quadratic forms $F_{γ }$ for quadratic irrationals $γ$, and then we determine the set of all integer solutions of the Diophantine equation $F_{γ }^{± k}(x,y)=± Q$.