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A generalization of Euler’s pentagonal number theorem

Far East Journal of Mathematical Sciences • 1996
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Publication Information
Authors Ahmed Abdel-Aziz
Keywords Not Available
Journal Far East Journal of Mathematical Sciences
Publisher Not Available
Volume 4
Issue 3
Pages 329-338
publication.type International
Paper Link Not Available
Supplementary Materials Not Available
Abstract
A connection between the theories of restricted partitions into parts congruent to 0 modulo m and unrestricted partitions is constructed here. According to this connection some congruence properties for restricted partitions are given and famous theorems are reformulated. In the first place, the author proves that the number of partitions of mn into parts congruent to 0 modulo m is equal to the number of partitions of n. In addition, a generalization of Euler’s pentagonal number theorem is easily expounded as a special case of Jacobi’s identity. This result is again proved elementary by developing a combinatorial argument due to Franklin.