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On the number of solutions of the equation (x1 + . . . + xn)m = ax1 . . . xn in a finite field
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Yu. N. Baulina
Veröffentlicht/Copyright:
1. Oktober 2004
We consider the equation (x1 + . . . + xn)m = ax1 . . . xn,
where a is a nonzero element of the finite field Fq, n ≥ 2, and m is a positive
integer. Explicit formulas for the number of solutions of this equation in 
under the condition d ∈ {1, 2, 3, 6}, where d = gcd(m – n, q – 1), are found. Moreover, we obtain formulas for the number of solutions for arbitrary d > 2 if there exists positive integer l such that d | (pl + 1), where p is the characteristic of Fq .
Published Online: 2004-10-01
Published in Print: 2004-10-01
Copyright 2004, Walter de Gruyter
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Artikel in diesem Heft
- Iteration-free decomposition of strongly dependent functions
- The shortest vectors of lattices connected with a linear congruent generator
- On the number of solutions of the equation (x1 + . . . + xn)m = ax1 . . . xn in a finite field
- On average and typical values of sums of pairwise distances for subsets of vertices of the n-dimensional unit cube
- Stability analysis of a strictly efficient solution of a vector problem of Boolean programming in the metric l1
- A family of multivariate χ2-statistics
- A representation of parastrophs of loops and quasigroups
Artikel in diesem Heft
- Iteration-free decomposition of strongly dependent functions
- The shortest vectors of lattices connected with a linear congruent generator
- On the number of solutions of the equation (x1 + . . . + xn)m = ax1 . . . xn in a finite field
- On average and typical values of sums of pairwise distances for subsets of vertices of the n-dimensional unit cube
- Stability analysis of a strictly efficient solution of a vector problem of Boolean programming in the metric l1
- A family of multivariate χ2-statistics
- A representation of parastrophs of loops and quasigroups
