Bernoulli numbers and the probability of a birthday surprise

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4 Scopus citations


A birthday surprise is the event that, given k uniformly random samples from a sample space of size n, at least two of them are identical. We show that Bernoulli numbers can be used to derive arbitrarily exact bounds on the probability of a birthday surprise. This result can be used in arbitrary precision calculators, and it can be applied to better understand some questions in communication security and pseudorandom number generation.

Original languageEnglish
Pages (from-to)657-663
Number of pages7
JournalDiscrete Applied Mathematics
Issue number3
StatePublished - 1 May 2003


  • Arbitrary precision calculators
  • Bernoulli numbers
  • Birthday paradox
  • Power sums
  • Pseudorandomness


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