On a kind of character sums and their recurrence properties. (English) Zbl 1417.11137
Let \(p>2\) be a prime and let \(\chi_2\) be the Legendre symbol modulo \(p\). Define \[ A_k(p)=\mathop{\sum_{a_1=1}^{p-1}\sum_{a_2=1}^{p-1}\cdots\sum_{a_k=1}^{p-1}}_{a_1^3+a_2^3+\cdots+a_k^3\equiv 0 (\bmod p)} \chi_2\left(a_1a_2\cdots a_k\right). \] This paper obtained a few identities for \(A_k(p)\) under certain conditions.
Reviewer: Huaning Liu (Shaanxi)
MSC:
| 11L40 | Estimates on character sums |
| 11L10 | Jacobsthal and Brewer sums; other complete character sums |
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