Iterative Methods for Pairs of Additive Diophantine Equations

Let k and n be integers with k ≥ n ≥ 1, and let c ₁, …, c_s and d ₁, …, d_s be non-zero integers. We consider the problem of determining conditions under which one can demonstrate that the system of equations (1.1) https://www.w3.org/1998/Math/MathML"> c 1 x 1 k + ⋯ + c s x s k = 0 d 1 x 1 n + ⋯ + d s x s n = 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780138747022/abb99e87-ffb7-4196-a4c4-acb0033e3d6a/content/eq1535.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>