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- W2005722215 abstract "One of the most important questions in number theory is to find properties on a system of equations that guarantee solutions over a field. A well-known problem is Waring's problem that is to find the minimum number of variables such that the equation x1d+⋯+xnd=β has solution for any natural number β. In this note we consider a generalization of Waring's problem over finite fields: To find the minimum number δ(k,d,pf) of variables such that a systemx1k+⋯+xnk=β1,x1d+⋯+xnd=β2 has solution over Fpf for any (β1,β2)∈Fpf2. We prove that, for p>3, δ(1,pi+1,pf)=3 if and only if f≠2i. We also give an example that proves that, for p=3, δ(1,3i+1,3f)⩾4." @default.
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- W2005722215 date "2008-07-01" @default.
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- W2005722215 title "On systems of linear and diagonal equation of degree <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msup><mml:mi>p</mml:mi><mml:mi>i</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math> over finite fields of characteristic p" @default.
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- W2005722215 doi "https://doi.org/10.1016/j.ffa.2007.09.008" @default.
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