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首页> 外文期刊>INTEGERS: electronic journal of Combinatorial Number Theory >THE SIGNUM EQUATION FOR ERDOS-SUR ? ANYI ′ SEQUENCES
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THE SIGNUM EQUATION FOR ERDOS-SUR ? ANYI ′ SEQUENCES

机译:Erdos-sur的Signum方程? Anyi'序列

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摘要

For an Erd?os-Sur′anyi sequence it is customary to consider its signum equation. Based on some classical heuristic arguments, we conjecture the asymptotic behavior for the number of solutions of this signum equation in the case of the sequence {nk}n (k 2) and the sequence of primes. Surprisingly, we show that this method does not apply at all for the Fibonacci sequence. By computing the precise number of solutions, in this case, we obtain an exponential growth, which shows, in particular, the limitations of such an intuition.
机译:对于ERD?OS-SUR'ANYI序列,习惯于考虑其SIGNUM方程。基于一些经典的启发式争论,我们在序列{nk} n(k2)和序列序列的情况下,猜测该Signum方程的解数的渐近行为。令人惊讶的是,我们表明这种方法根本不适用于斐波纳契序列。通过计算精确的解决方案,在这种情况下,我们获得指数增长,特别是尤其显示这种直觉的局限性。

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