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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
Published/Copyright:
October 1, 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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Articles in the same Issue
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- The shortest vectors of lattices connected with a linear congruent generator
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- On average and typical values of sums of pairwise distances for subsets of vertices of the n-dimensional unit cube
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