Rational and algebraic approximations of algebraic numbers and their application.

Autor: Yuan, Pingzhi
Zdroj: Science in China. Series A: Mathematics, Physics & Astronomy; Oct1997, Vol. 40 Issue 10, p1045-1051, 7p
Abstrakt: Effective rational and algebraic approximations of a large class of algebraic numbers are obtained by Thue-Siegel’s method. As an application of this result, it is proved that: if D>0 is not a square, and ε = x 0 denotes the fundamental solution of x 2− Dy 2=−1, then x 2+1= Dy 4 is solvable if and only if y 0= A 2, where A is an integer. Moreover, if ε>64, then x 2+1= Dy 4 has at most one positive integral solution ( x, y). [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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