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Paper IPM / M / 16496  


Abstract:  
Let \cX be the nonsingular model of a
plane curve of type y^{n}=f(x) over the finite field \F
of order q^{2}, where f(x) is a separable polynomial of
degree coprime to n. If the number of \Frational
points of \cX attains the HasseWeil bound, then the
condition n divides q+1 is equivalent to the
solubility of f(x) in \F []. In this paper, we
investigate this condition for f(x)=x^{l}(x^{m}+1).
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