On sets which contain a qth power residue for almost all prime modules

• Autorzy: Mariusz Ska/lba
• Języki publikacji: EN

Abstrakty

EN

A classical theorem of M. Fried [2] asserts that if non-zero integers $β₁,...,β_l$ have the property that for each prime number p there exists a quadratic residue $β_j$ mod p then a certain product of an odd number of them is a square. We provide generalizations for power residues of degree n in two cases: 1) n is a prime, 2) n is a power of an odd prime. The proofs involve some combinatorial properties of finite Abelian groups and arithmetic results of [3].

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2005
• Tom: 102
• Numer: 1
• Strony: 67-71

Daty

wydano

2005

Twórcy

autor

Mariusz Ska/lba

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

Identyfikatory

DOI

10.4064/cm102-1-6