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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
##### Keywords:
polynomial congruences; number of solutions
Full Text:
##### References:
 [1] JAKUBEC J.: The congruence for Gauss’s period. J. Number Theory · Zbl 0807.11049
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