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On the parity of generalized partition functions, III

Fethi Ben Saïd, Jean-Louis Nicolas, Ahlem Zekraoui (2010)

Journal de Théorie des Nombres de Bordeaux

Improving on some results of J.-L. Nicolas [15], the elements of the set 𝒜 = 𝒜 ( 1 + z + z 3 + z 4 + z 5 ) , for which the partition function p ( 𝒜 , n ) (i.e. the number of partitions of n with parts in 𝒜 ) is even for all n 6 are determined. An asymptotic estimate to the counting function of this set is also given.

On the powerful part of n 2 + 1

Jan-Christoph Puchta (2003)

Archivum Mathematicum

We show that n 2 + 1 is powerfull for O ( x 2 / 5 + ϵ ) integers n x at most, thus answering a question of P. Ribenboim.

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