Abstract
We consider the equation (*) xp+yp+zp=0, where p is an odd prime and x, y, z are non-zero rational integers prime to each other. The study of the equation (*) is usually subdivided into two cases: (I) p ⫮ xyz, (II) p|xyz. In the present paper we shall treat the case (I) of the equation (*) and derive some consequences from the criteria of Kummer and Mirimanoff.
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