Affiliation:
1. School of Mathematics and Statistics, Arizona State University, Tempe AZ 85287-1804, USA
2. Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30 - 348 Kraków, Poland
Abstract
It is well known that the Diophantine equations x4 + y4 = z4 + w4 and x4 + y4 + z4 = w4 each have infinitely many rational solutions. It is also known for the equation x6 + y6 - z6 = w2. We extend the investigation to equations xa ± yb = ±zc ± wd, a, b, c, d ∈ Z, with 1/a + 1/b + 1/c + 1/d = 1. We show, with one possible exception, that if there is a solution of the equation in the reals, then the equation has infinitely many solutions in the integers. Of particular interest is the equation x6 + y6 + z6 = w2 because of its classical nature; but there seem to be no references in the literature.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
3 articles.
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