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Bernoulli numbers and exact covering systems. (English) Zbl 0776.11008
It is proved that a set of arithmetic progressions $$A=\bigl\{b_ i\pmod{a_ j};\;1\leq j\leq n\bigr\}$$ is an exact covering system with $$b_ 1=0$$ and $$0\leq b_ j< a_ j$$ if and only if the reciprocals of the $$a_ j$$’s sum to 1 and the $$a_ j$$, $$b_ j$$ generate an interesting recurrence for Bernoulli numbers. The recurrences thus obtained generalize the one found by E. Deeba and D. Rodriguez [Am. Math. Mon. 98, 423-426 (1991; Zbl 0743.11012)].

##### MSC:
 11B68 Bernoulli and Euler numbers and polynomials 11A07 Congruences; primitive roots; residue systems 11B25 Arithmetic progressions
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