On the Number of Solutions of Some Trinomial Equations in a Finite Field | Zendy

Loo-Keng Hua | Zendy; H. S. Vandiver | Zendy

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On the Number of Solutions of Some Trinomial Equations in a Finite Field

Author(s) -

Loo-Keng Hua,

H. S. Vandiver

Publication year - 1949

Publication title -

proceedings of the national academy of sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.011

H-Index - 771

eISSN - 1091-6490

pISSN - 0027-8424

DOI - 10.1073/pnas.35.8.477

Subject(s) - trinomial , adaptation (eye) , climate change , sustainability , field (mathematics) , macro , sustainability science , computer science , management science , ecology , mathematics , economics , psychology , biology , pure mathematics , discrete mathematics , neuroscience , sustainability organizations , programming language

in xl and x2, non-zero elements of a finite field F(p') of order pn, p an odd prime with C1, C2, C3 given elements of F(p'), c1c2c3 $ 0, in certain special cases. Secondly, we shall find limits (Theorem II) for the number of solutions of (1) which are better than those given in C for the solutions of this particular equation, and which have the unusual property that they agree with the exact values found for the number of solutions in the special cases treated in Theorem I. We shall employ the notation used in H (defined in (9b) just below relation (14) of that paper). Let a be a primitive (dsls2)-th root of unity, m = ds1s2 where ds, = k12 ds2 = k2 where (k1, k2) = d, whence (sl, s2) = 1. Let X-1 be a special kicharacter and xt, a special k2-character in F(p') and write, if K stands for F(p'),

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