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 On lacunary recurrences with gaps of length four and eight for the Bernoulli numbers Bull. Korean Math. Soc.Published online 2018 Nov 07 Mircea Merca Academy of Romanian Scientists Abstract : The problem of finding fast computing methods for Bernoulli numbers has a long and interesting history. In this paper, the author provides new proofs for two lacunary recurrence relations with gaps of length four and eight for the Bernoulli numbers. These proofs invoked the fact that the $n$th powers of $\pi^2$, $\pi^4$ and $\pi^8$ can be expressed in terms of the $n$th elementary symmetric functions. Keywords : Bernoulli numbers, recurrences MSC numbers : 11B68, 11B37, 05E05 Full-Text :