Browsing by Author "Liptai, Kalman"

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    Resolution of the equation (3 x 1-1)(3x2-1) = (5y1-1)(5y2-1)
    (Rocky Mt Math Consortium, 2020-08-01) Liptai, Kalman; Nemeth, Laszlo; Soydan, Gökhan; Szalay, Laszlo; SOYDAN, GÖKHAN; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-6321-4132; M-9459-2017
    Consider 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.