On Alternatives of Polynomial Congruences
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 2, pp. 123-132
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
What should be assumed about the integral polynomials
$f_{1}(x),\ldots,f_{k}(x)$ in order that the solvability of the
congruence $f_{1}(x)f_{2}(x)\cdots f_{k}(x)\equiv
0\pmod{p}$ for sufficiently large primes $p$ implies the
solvability of the equation $f_{1}(x)f_{2}(x)\cdots
f_{k}(x)=0$ in integers $x$? We provide some explicit
characterizations for the cases when $f_j(x)$ are binomials or
have cyclic splitting fields.
Mots-clés :
what should assumed about integral polynomials ldots order solvability congruence cdots equiv pmod sufficiently large primes implies solvability equation cdots integers provide explicit characterizations cases binomials have cyclic splitting fields
Affiliations des auteurs :
Mariusz Skałba 1
@article{10_4064_ba52_2_3,
author = {Mariusz Ska{\l}ba},
title = {On {Alternatives} of {Polynomial} {Congruences}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {123--132},
publisher = {mathdoc},
volume = {52},
number = {2},
year = {2004},
doi = {10.4064/ba52-2-3},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba52-2-3/}
}
TY - JOUR AU - Mariusz Skałba TI - On Alternatives of Polynomial Congruences JO - Bulletin of the Polish Academy of Sciences. Mathematics PY - 2004 SP - 123 EP - 132 VL - 52 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/ba52-2-3/ DO - 10.4064/ba52-2-3 LA - fr ID - 10_4064_ba52_2_3 ER -
Mariusz Skałba. On Alternatives of Polynomial Congruences. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 2, pp. 123-132. doi: 10.4064/ba52-2-3
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