The number of solutions to the generalized Pillai equation \pm r a^x \pm s b^y = c.
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چکیده
منابع مشابه
The Number of Solutions to the Generalized Pillai Equation ±ra
x ± sb y = c. Abstract We consider N , the number of solutions (x, y, u, v) to the equation (−1) u ra x + (−1) v sb y = c in nonnegative integers x, y and integers u, v ∈ {0, 1}, for given integers a > 1, b > 1, c > 0, r > 0 and s > 0. When gcd(ra, sb) = 1, we show that N ≤ 3 except for a finite number of cases all of which satisfy max(a, b, r, s, x, y) < 2 · 10 15 for each solution; when gcd(a...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2013
ISSN: 1246-7405,2118-8572
DOI: 10.5802/jtnb.832