期刊名称：Constantin Brancusi University's Annals, Letters and Social Sciences Serie
印刷版ISSN：1844-6051
出版年度：2010
期号：3
出版社：Academica Brancusi Publisher
摘要：Find the problem : det A = 1, the ( 1) 1 2 2 lim − = →∞ ⎠ ⎞ ⎝ ⎛ + ∏ n a e n k n k n k and show that the sequence ( ) * n n N x ∈ is periodic . Key words: own values , limit , sequence 1. Let the crowd ( ) * A∈ Mn Z ,n ∈ N and p,q,r natural numbers with r ≡ 1(mod 2) and 2 2 2 p = q + r . If n P q p A q A r I 2 2 2 2 2 = + , then det A = 1 . Solution. We consider the function ( ) 2 2 2 2 2 f x p x q x r P q = − − , f : R → R . (1) Observe that: f ′ (x) ⎦ ⎤ ⎣ ⎡ ⎠ ⎞ ⎝ ⎛ = − − 4 4 1 2 2 p q p x x q r The roots of equation f ′ (x)= 0 are 0 x 1 = and 2 4 2 r p q x ⎠ ⎞ ⎝ ⎛ = ( r ≠ 0 and q ≠ 1) . Variation table of function f ( ) x is ( 0 < < 1 p q ) :
