On Alternatives of Polynomial Congruences

• Autorzy: Mariusz Skałba
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11A15: Power residues, reciprocity
• 11R20: Other abelian and metabelian extensions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: 52
• Numer: 2
• Strony: 123-132

Daty

wydano

2004

Twórcy

autor

Mariusz Skałba

• Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba52-2-3