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• # Artykuł - szczegóły

## Bulletin of the Polish Academy of Sciences. Mathematics

2011 | 59 | 2 | 115-119

## Solution to a Problem of Lubelski and an Improvement of a Theorem of His

EN

### Abstrakty

EN
The paper consists of two parts, both related to problems of Lubelski, but unrelated otherwise. Theorem 1 enumerates for a = 1,2 the finitely many positive integers D such that every odd positive integer L that divides x² +Dy² for (x,y) = 1 has the property that either L or $2^{a}L$ is properly represented by x²+Dy². Theorem 2 asserts the following property of finite extensions k of ℚ : if a polynomial f ∈ k[x] for almost all prime ideals 𝔭 of k has modulo 𝔭 at least v linear factors, counting multiplicities, then either f is divisible by a product of v+1 factors from k[x]∖ k, or f is a product of v linear factors from k[x].

115-119

wydano
2011

### Twórcy

autor
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland