Theorems · Theorem · number theory
Int.erdos_ginzburg_ziv_multiset
∀ {n : ℕ} (s : Multiset ℤ), 2 * n - 1 ≤ s.card → ∃ t ≤ s, t.card = n ∧ ↑n ∣ t.sumThe Erdős–Ginzburg–Ziv theorem for ℤ for multiset.
Any multiset of at least 2 * n - 1 elements of ℤ contains a submultiset of n elements whose
sum is divisible by n.
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- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
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- Finsetproof · cited by 13,712
- Finset.sumproof · cited by 5,195
- Multisetstatement and proof · cited by 2,627
- Finset.cardproof · cited by 2,327
- Multiset.mapproof · cited by 876
- Finset.valproof · cited by 438
- Multiset.sumstatement · cited by 388
- Multiset.cardstatement and proof · cited by 375
- Multiset.card_mapproof · cited by 57
- Multiset.toEnumFinsetproof · cited by 24
- Multiset.map_fst_le_of_subset_toEnumFinsetproof · cited by 3
- Multiset.card_toEnumFinsetproof · cited by 3
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