A pr 2 00 6 TWO S - UNIT EQUATIONS WITH MANY SOLUTIONS
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چکیده
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, and R. Tijdeman showed that there exist arbitrarily large sets S such that the S-unit equation a + b = c has more than exp((4− ǫ) √
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تاریخ انتشار 2007