Non-triviality of a product in the Adams E 2-term

Let p be a prime greater than five and A the mod p Steenrod algebra. In this paper, we prove that (h_n h_m tilde delta _{s + 4} in Ext_A^{s + 6,t(s,n,m) + s} (Z/p,Z/p)) is nontrivial in the Adams E₂-term when m ≥ n + 2 ≥ 7 and 0 ≤ s < p ? 4, and trivial in the Adams E₂-term when m ≥ n + 2 = 6 and 0 ≤ s < p ? 4, where (tilde delta _{s + 4} ) stands for the fourth Greek letter element and t(s, n, m) = 2(p ? 1)[(s + 1) + (s + 2)p + (s + 3)p² + (s + 4)p³ + pⁿ + p^m].