ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXI, 1(2002)
p. 113

A CLASS OF ALGEBRAIC-EXPONENTIAL CONGRUENCES MODULO $p$
C. Cobeli, M. Vajaitu and A. Zaharescu

Abstract.  Let $p$ be a prime number, $\J$ a set of consecutive integers, $\overline \FF _p$ the algebraic closure of $\FF _p=\ZZ /p\ZZ$ and $\C$ an irreducible curve in an affine space $\AA^r(\overline \FF _p),$ defined over $\FF _p$. We provide a lower bound for the number of $r-$tuples $(x,y_1,\dots,y_ r-1 )$ with $x \in \J,$ $y_1,\dots,y_ r-1 \in 0,1,\cdots,p-1$ for which $(x, y_1^x,\dots,$ $y_ r-1 ^x)$ (mod $p$) belongs to $\C( \FF _p).$

AMS subject classification:  11T99
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