Liptai, KalmanNemeth, LaszloSoydan, GökhanSzalay, Laszlo2024-07-262024-07-262020-08-010035-7596https://doi.org/10.1216/rmj.2020.50.1425https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-50/issue-4/Resolution-of-the-equation-3x_1-13x_2-15y_1-15y_2-1/10.1216/rmj.2020.50.1425.shorthttps://arxiv.org/pdf/2001.09717https://hdl.handle.net/11452/43472Consider the diophantine equation (3(x1) - 1)(3(x2) - 1) = (5(y1) - 1)(5(y2) - 1) in positive integers x(1) <= x(2) and y(1) <= y(2). Each side of the equation is a product of two terms of a given binary recurrence. We prove that the only solution to the title equation is (x(1), x(2), y(1), y(2)) = (1, 2, 1, 1). The main novelty of our result is that we allow products of two terms on both sides.eninfo:eu-repo/semantics/closedAccessFibonacciNumbersExponential diophantine equationLinear recurrenceBaker methodScience & technologyPhysical sciencesMathematicsArticle0005763376000171425143350410.1216/rmj.2020.50.14251945-3795