On the equation (x_1^{m_1}+...+x_n^{m_n})^k=ax_1...x_n over a finite fieldстатья
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Дата последнего поиска статьи во внешних источниках: 11 мая 2017 г.
Аннотация:Let N_q be the number of solutions to the equation
(x_1^{m_1}+...+x_n^{m_n})^k=ax_1...x_n
over the finite field F_q = F_(p^s). Carlitz found formulas for N_q when m_1 = ⋯ = m_n = 1, k = 2, n = 3 or 4,
p > 2; and when m_1 = ⋯ = m_n = 2, k = 1, n = 3 or 4, p > 2. In earlier papers, we obtained some generalizations of Carlitz's results. In this paper, we find formulas for N_q when -1 is a power of p modulo dD, where D = lcm[d_1,…,d_n], , M = lcm[m_1,…,m_n], d_j = gcd(m_j,q - 1), 1 ≤ j ≤ n.