Publication:
Resolution of the equation (3 x 1-1)(3x2-1) = (5y1-1)(5y2-1)

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2020-08-01

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Rocky Mt Math Consortium

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Abstract

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.

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Fibonacci, Numbers, Exponential diophantine equation, Linear recurrence, Baker method, Science & technology, Physical sciences, Mathematics

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