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Note on the number of solutions of the congruence \(f(x_ 1,x_ 2,\dots, x_ n)\equiv 0\pmod p\). (English) Zbl 0816.11027

Let \(f\) be a polynomial in \(n\) variables with integer coefficients and let \(p>2\) be a prime. Consider the number \(N_ p\) of solutions of the congruence \[ f(x_ 1, \dots, x_ n) \equiv 0\pmod p, \qquad x_ 1\dots x_ n\not\equiv 0\pmod p. \] The paper presents an explicit expression for \(N_ p \pmod p\). The main tool of the proof is a recent result of the author [J. Number Theory 48, No. 1, 36-45 (1994; Zbl 0807.11049)].
Reviewer: I.Gaál (Debrecen)

MSC:

11D79 Congruences in many variables

Citations:

Zbl 0807.11049
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References:

[1] JAKUBEC J.: The congruence for Gauss’s period. J. Number Theory · Zbl 0807.11049
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