具有斐波那契分量的马尔科夫-罗森伯格三元组

Pub Date : 2020-06-12 DOI:10.3336/gm.55.1.03

Szabolcs Tengelys

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引用次数: 4

摘要

。刻画了Markoff-Rosenberger方程ax 2 + × 2 + cz2 = dxyz的解，条件是a,b,c,d∈Z, gcd(a,b) = gcd(a,c) = gcd(a,c) = 1和a,b,c | d，其中(x,y, Z) = (Fi,F j,F k)，其中F n表示任意整数n≥0时的第n个斐波那契数。

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Markoff-Rosenberger triples with Fibonacci components

. We characterize the solutions of the Markoﬀ-Rosenberger equation ax 2 + by 2 + cz 2 = dxyz with a,b,c,d ∈ Z , gcd( a,b ) = gcd( a,c ) = gcd( b,c ) = 1 and a,b,c | d , for which ( x,y,z ) = ( F i ,F j ,F k ) , where F n denotes the n -th Fibonacci number for any integer n ≥ 0 .

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