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Erdős problem 541

Let a1,…,apa_1, \dots, a_p be (not necessarily distinct) residues modulo a prime pp, such that there exists some rr so that if S⊆[p]S \subseteq [p] is non-empty and ∑i∈Sai≡0(modp)\sum_{i \in S} a_i \equiv 0 \pmod{p} then ∣S∣=r|S| = r.

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