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We discuss the form of certain algebraic continued fractions in the field ofpower series over $F_p$, where p is an odd prime number. This leads to giveexplicit continued fractions in these fields, satisfying an explicit algebraicequation of arbitrary degree $d\geq 2$ and having an irrationality measureequal to $d$. Our results are based on a mysterious finite sequence of rationalnumbers.

On particular families of hyperquadratic continued fractions in power series fields of odd characteristic