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A generalization of Euler’s pentagonal number theorem

Far East Journal of Mathematical Sciences • 1996
العودة
معلومات البحث
المؤلفون Ahmed Abdel-Aziz
الكلمات المفتاحية Not Available
المجلة العلمية Far East Journal of Mathematical Sciences
الناشر Not Available
المجلد 4
العدد 3
الصفحات 329-338
publication.type International
رابط البحث Not Available
المواد المرفقة Not Available
الملخص
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.
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