Perfect Powers in Smarandache Type Expressions
نویسنده
چکیده
In [2] and [31 the authors ask how many primes are of the Smarandache form (see [10]) x Y + yX, where gcd (x, y) = 1 and x, y ~ 2. In [6] the author showed that there are only finitely many numbers of the above form which are products of factorials. In this article we propose the following Conjecture 1. Let a, b, and c be three integers with ab i= O. Then the equation with x, y, n ~ 2, and gcd (x, y) = 1, has finitely many solutions (x, y, z, n). We announce the following result: Theorem 1. The "abc Conjecture" implies Conjecture 1.
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