Diagonal diophantine equations with small prime variables

摘要

Let (a(i), a(j)) = 1, 1 <= i < j <= s and s = 2(k) + 1, where a(1), ... , a(s), s and k >= 4 are nonzero integers. In this paper, we show that if the diagonal diophantine equation a(1)p(1)(k) + ... + a(s)p(s)(k) = n is satisfying some necessary conditions, then we have the following results: For any epsilon > 0, we have