ON TRINOMIAL EQUATIONS IN A FINITE FIELD

On Trinomial Equations in a Finite Field.

where g is a multiplicative generator of the nonzero elements of F [pfn; i is a fixed integer in the set 0, 1, . . ., c 1; j is a fixed integer in the set 0, 1, .m. ., 1; pf _ 1 = cm; s isin the range 0, 1, . . ., m -1; t is in the range 0, 1, ..., c 1. Let the number of sets of solutions s, t of the above type be (i, j),m. Then (noting relation (2) of the present paper) the maximum value for (...

On Cyclotomic Relations and Trinomial Equations in a Finite Field.

this subject had not been sufficiently developed, as far as possible applications to number theory were concerned, at the time he wrote his report. Hilbert also said that he was very glad to hear that Fueter had fashioned the necessary tools from the theory of elliptic functions to yield an advanced theory of quadratic fields. We hope to be able to discuss in a later paper the methods of Fueter...

Cyclotomy and Trinomial Equations in a Finite Field.

On the Properties of Certain Trinomial Equations in a Finite Field.

In a recent paper' Mrs. E. H. Pearson and the writer considered certain types of trinomial congruences, and in later papers the writer2 3 developed this topic further and pointed out2 a relation of such questions to Case II of Fermat's Last Theorem. In the present paper we shall continue this investigation. Let p be an odd prime and F[pn] denote a finite field of order pf, and consider the solu...

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

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 va...