Naofumi Kimura

Rational functions that satisfy fn + gn + hn = 1

Solutions of non-constant rational functions of the Fermat type functional equations ( ⁎ ) f n + g n + h n = 1 , where n ≥ 2 are integers, are considered in the complex plane. It is known that ( ⁎ ) cannot possess non-constant rational function solutions when n ≥ 8 , and that the...