An Additive Problem in Finite Fields with Powers of Elements of Large Multiplicative Order
نویسندگان
چکیده
For a given finite field Fq, we study sufficient conditions to guarantee that the set {θ 1 + θ y 2 : 1 ≤ x ≤ M1, 1 ≤ y ≤ M2} represents all the nonzero elements of Fq. We investigate the same problem for θ 1 − θ y 2 and as a consequence we prove that any element in the finite field of q elements has a representation of the form θ − θ, 1 ≤ x, y ≤ √ 2q whenever θ has multiplicative order at least √ 2q. This improves the previous known bound for a question possed by A. Odlyzko.
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تاریخ انتشار 2013