Carlitz’s Theorem
نویسنده
چکیده
A couple of years later, Carlitz [6] refined this theorem a little basically by dropping the conditions that f(0) = 0 and f(1) = 1 and by allowing f(a)−f(b) a−b to always be a square or always be a nonsquare, whenever a 6= b. He then accordingly modified the conclusion to f(x) = ax + b with a being a square or nonsquare according to which f(a)−f(b) a−b was. Now a change of notation. Let F = GF (q), where q is a power of an odd prime. Let E = {x ∈ F |x = 1} = {±1}
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