The generalized fermat conjecture

Abstract. If a; b; c are non-zero integers, we considerer the following problem: for which values of n the line ax + by + cz = 0 may be tangent to the curve xn + yn = zn? We give a partial solution: if n = 5 or if n - 1 is a prime a number, then the answer is the line cannot be tangent to the curve....