This was proved by Erdős and Szemerédi [ErSz76] for p sufficiently large.
[ErSz76] Erd\H os, E. and Szemerédi, E., On a problem of Graham.
Publ. Math. Debrecen (1976), 123--127.
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theorem erdos_541.variants.large_primes : ∀ᶠ p in atTop, p.Prime → ∀ a : Fin p → ZMod p,
(∃ r, ∀ (S : Finset (Fin p)), S ≠ ∅ → ∑ i ∈ S, a i = 0 → S.card = r) →
(Set.range a).ncard ≤ 2
