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Języki publikacji
Abstrakty
Let K be a field, a,b ∈ K and ab ≠ 0. Consider the polynomials g₁(x) = xⁿ+ax+b, g₂(x) = xⁿ+ax²+bx, where n is a fixed positive integer. We show that for each k≥ 2 the hypersurface given by the equation
$S_{k}^{i}: u² = ∏_{j=1}^{k} g_{i}(x_{j})$, i=1,2,
contains a rational curve. Using the above and van de Woestijne's recent results we show how to construct a rational point different from the point at infinity on the curves $C_{i}:y² = g_{i}(x)$, (i=1,2) defined over a finite field, in polynomial time.
$S_{k}^{i}: u² = ∏_{j=1}^{k} g_{i}(x_{j})$, i=1,2,
contains a rational curve. Using the above and van de Woestijne's recent results we show how to construct a rational point different from the point at infinity on the curves $C_{i}:y² = g_{i}(x)$, (i=1,2) defined over a finite field, in polynomial time.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
97-104
Opis fizyczny
Daty
wydano
2007
Twórcy
autor
- Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-2-1