اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAn identity involving number of representations of $n$ as a sum of $r$ triangular numbers
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تأليف
Sumit Kumar Jha
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Let $sum_{d|n}$ denote sum over divisors of a positive integer $n$, and $t_{r}(n)$ denote the number of representations of $n$ as a sum of $r$ triangular numbers. Then we prove that $$ sum_{d|n}frac{1+2,(-1)^{d}}{d}=sum_{r=1}^{n}frac{(-1)^{r}}{r}, binom{n}{r}, t_{r}(n) $$ using a result of Ono, Robbins and Wahl.
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