It is established that for every pair of additive forms $f=\sum_{i=1}^s a_i x_i^k, g=\sum_{i=1}^s b_i x_i^k$ of degree $k$ in $s>2k^2$ variables the equations $f=g=0$ have a non-trivial $p$-adic solution for all odd primes $p$.
Artin's Conjecture on Zeros of $p$-Adic Forms
On Artin's conjecture: linear slices of diagonal hypersurfaces
Finite Planes, Zigzag Sequences, Fibonacci Numbers, Artin's Conjecture and Trinomials
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