Abstract
In the paper, the additive complexity of matrices formed by positive integer powers of greatest common divisors and least common multiples of the indices of the rows and columns is considered. It is proved that the complexity of the n × n matrix formed by the numbers GCDr(i, k) over the basis {x + y} is asymptotically equal to rn log2 n as n→∞, and the complexity of the n × n matrix formed by the numbers LCMr(i, k) over the basis {x + y,−x} is asymptotically equal to 2rn log2 n as n→∞.
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Original Russian Text © S. B. Gashkov, I. S. Sergeev, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 2, pp. 196–211.
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Gashkov, S.B., Sergeev, I.S. On the additive complexity of GCD and LCM matrices. Math Notes 100, 199–212 (2016). https://doi.org/10.1134/S0001434616070166
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DOI: https://doi.org/10.1134/S0001434616070166