On Alternatives of Polynomial Congruences

Mariusz Skałba

Mariusz Skałba

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004), p. 123-132 / Harvested from The Polish Digital Mathematics Library

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Résumé

What should be assumed about the integral polynomials $f ₁ (x), . . ., f_{k} (x)$ in order that the solvability of the congruence $f ₁ (x) f ₂ (x) \dots f_{k} (x) \equiv 0 (m o d p)$ for sufficiently large primes p implies the solvability of the equation $f ₁ (x) f ₂ (x) \dots f_{k} (x) = 0$ in integers x? We provide some explicit characterizations for the cases when $f_{j} (x)$ are binomials or have cyclic splitting fields.

Publié le : 2004-01-01

Zbl 1107.11003

EUDML-ID : urn:eudml:doc:280864

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Mariusz Skałba. On Alternatives of Polynomial Congruences. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 123-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-2-3/