On systems of Diophantine equations with a large number of integer solutions

الأصل · EN

Let Eₙ=xᵢ+xⱼ=xₖ, xᵢ · xⱼ=xₖ: i,j,k ∈ 1,...,n. For each integer n ≥ 13, J. Browkin defined a system Bₙ Eₙ which has exactly bₙ solutions in integers x₁,...,xₙ, where bₙ ∈ N{0 and the sequence bₙₙ₌₁₃∞ rapidly tends to infinity. For each integer n ≥ 12, we define a system Tₙ Eₙ which has exactly tₙ solutions in integers x₁,...,xₙ, where tₙ ∈ N{0 and limₙ → ∞ tₙ/bₙ=∞.