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- W2023338413 abstract "Abstract Let n be a positive integer. In this paper, using the results on the existence of primitive divisors of Lucas numbers and some properties of quadratic and exponential diophantine equations, we prove that if n ≡ 3 (mod 6), then the equation x 2 + (3n 2 + 1)y = (4n 2 + 1)z has only the positive integer solutions (x, y, z) = (n, 1, 1) and (8n 3 + 3n, 1, 3)." @default.
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- W2023338413 date "2014-10-01" @default.
- W2023338413 modified "2023-09-25" @default.
- W2023338413 title "The exponential Diophantine equation x2 + (3n 2 + 1)y = (4n 2 + 1)z" @default.
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- W2023338413 doi "https://doi.org/10.2478/s12175-014-0265-z" @default.
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