Tackling Markoff-Hurwitz Equations

摘要

We present algorithms for searching and generating solutions to the equation x12+x22+ ...+xn2 = kx1x2...xn. Solutions are reported for n = 2, 3,..., 9. Properties of solutions are discussed. We can prove that the solutions do not exist when n=4 and k=2 or 3, n=5 and k=2 or 3. Conjectures based on computational results are discussed.