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Congruences on the number of restricted \(m\)-ary partitions. (English) Zbl 1343.05029

Summary: G. E. Andrews et al. [“Arithmetic properties of \(m\)-ary partitions without gaps”, Ann. Comb. (to appear)] proved an infinite family of congruences on the number of the restricted \(m\)-ary partitions when \(m\) is a prime. In this note, we show that these congruences hold for arbitrary positive integer \(m\) and thus confirm the conjecture of Andrews, et al. [loc. cit.].

MSC:

05A17 Combinatorial aspects of partitions of integers
11P83 Partitions; congruences and congruential restrictions
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References:

[1] Andrews, G. E., Congruence properties of the m-ary partition function, J. Number Theory, 3, 104-110 (1971) · Zbl 0215.07002
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