The purpose of this article is to provide criteria for the solvability of the Diophantine equation a2X2− bY 2 = c in terms of the simple continued fraction expansion of √ a2b, and to explore criteria for the solvability of AX2 − BY 2 = C for given A, B, C ∈ N in the general case. This continues work in [9]–[11].

background and objectives: lamiaceae members have long been used in iranian traditional medicine (itm) for their various medicinal properties. the main objective of this study was to evaluate the antioxidant capacity and antimicrobial activity as well as the total phenolic content (tpc) of the various extracts and fractions of two iranian endemic micromeria (m. persica and m. hedgei). methods: ...