On Alternatives of Polynomial Congruences

Mariusz Skałba. "On Alternatives of Polynomial Congruences." Bulletin of the Polish Academy of Sciences. Mathematics 52.2 (2004): 123-132. <http://eudml.org/doc/280864>.

@article{MariuszSkałba2004,
abstract = {What should be assumed about the integral polynomials $f₁(x),...,f_\{k\}(x)$ in order that the solvability of the congruence $f₁(x)f₂(x) ⋯ f_\{k\}(x) ≡ 0 (mod p)$ for sufficiently large primes p implies the solvability of the equation $f₁(x)f₂(x) ⋯ f_\{k\}(x) = 0$ in integers x? We provide some explicit characterizations for the cases when $f_j(x)$ are binomials or have cyclic splitting fields.},
author = {Mariusz Skałba},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {binomial congruences; algebraic number fields},
language = {eng},
number = {2},
pages = {123-132},
title = {On Alternatives of Polynomial Congruences},
url = {http://eudml.org/doc/280864},
volume = {52},
year = {2004},
}

TY - JOUR
AU - Mariusz Skałba
TI - On Alternatives of Polynomial Congruences
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 2
SP - 123
EP - 132
AB - What should be assumed about the integral polynomials $f₁(x),...,f_{k}(x)$ in order that the solvability of the congruence $f₁(x)f₂(x) ⋯ f_{k}(x) ≡ 0 (mod p)$ for sufficiently large primes p implies the solvability of the equation $f₁(x)f₂(x) ⋯ f_{k}(x) = 0$ in integers x? We provide some explicit characterizations for the cases when $f_j(x)$ are binomials or have cyclic splitting fields.
LA - eng
KW - binomial congruences; algebraic number fields
UR - http://eudml.org/doc/280864
ER -