Pairs of additive sextic forms (Q1762303)

A special case of a conjecture commonly attributed to Emil Artin states that any system of two homogeneous diagonal forms of degree \(k\) with integer coefficients should have nontrivial solutions (i.e. at least one of the variables should be different from zero) in every \(p\)-adic field \(\mathbb{Q}_p\), provided only that the number of variables is at least \(2k^2+1\). In this article, the authors prove that the conjecture is true when \(k=6\).