Abstract
Let a, b, and n be non-z.ero integers with (a,b) = 1 and n ≥ 2. We show that the greatest prime factor of ax m + by n. where x, y, and m are non-zero integers satisfying (ax, by) = 1, ¦x¦> 1, and m ≥ 2, is not less than log m times an effectively computable positive constant depending only on a, b, and n.
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