منابع مشابه
A pr 2 00 6 TWO S - UNIT EQUATIONS WITH MANY SOLUTIONS
In this note we consider two S-unit equations for which we will exhibit many solutions. Our first problem concerns solutions to the equation a + b = c where a, b, and c are coprime integers such that all prime factors of abc lie in a given set S of s primes. In [8] J.-H. Evertse showed that this S-unit equation has at most exp(4s+ 6) solutions. On the other hand, in [6] P. Erdős, C. Stewart, an...
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The existence of time periodic solutions of nonlinear wave equations utt −∆nu + ` n− 1 2 ́2 u = g(u)− f(t, x) on n-dimensional spheres is considered. The corresponding functional of the equation is studied by the convexity in suitable subspaces, minimax arguments for almost symmetric functional, comparison principles and Morse theory. The existence of infinitely many time periodic solutions is o...
متن کاملSome Ramanujan–Nagell equations with many solutions
If we fix y as 1 in (1) we obtain a Ramanujan-Nagell equation. In [4] Erdös, Stewart and Tijdeman proved that the exponential dependence on s in estimates (2) and (3) is not far from the truth by giving examples of Ramanujan-Nagell equations with many solutions. Let ε be a positive number, let 2 = p1, p2, . . . be the sequence of prime numbers and let n be an integer with n ≥ 2. They proved tha...
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We shall prove that if F is a cubic binary form with integer coefficients and non-zero discriminant then there is a positive number c, which depends on F, such that the Thue equation F (x, y) = m has at least c(logm) solutions in integers x and y for infinitely many positive integers m.
متن کاملDetermining the small solutions to S-unit equations
In this paper we generalize the method of Wildanger for nding small solutions to unit equations to the case of S-unit equations. The method uses a minor generalization of the LLL based techniques used to reduce the bounds derived from transcendence theory, followed by an enumeration strategy based on the Fincke-Pohst algorithm. The method used reduces the computing time needed from MIPS years d...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2007
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.07.017