2024-11-042024-11-042018-01-010037-8712https://doi.org/10.5269/bspm.v36i3.30799https://hdl.handle.net/11452/47328Let 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-gamma and indefinite quadratic forms F-gamma for quadratic irrationals gamma, and then we determine the set of all integer solutions of the Diophantine equation F-gamma(+/- k) (x, y) = +/- Q.eninfo:eu-repo/semantics/closedAccessQuadratic idealsIndefinite quadratic formsDiophantine equationsScience & technologyPhysical sciencesMathematicsArticle00045896020001317319236310.5269/bspm.v36i3.30799