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Our result implies that \\Sigma(A) = Z/nZ for every set A of units of Z/nZ with |A| >= 8 \\sqrt{n}. This consequence was first proved by Erd\\H{o}s and Heilbronn for n prime, and by Vu (with a weaker constant) for general n."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0612045","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-12-02T04:20:48Z","cross_cats_sorted":[],"title_canon_sha256":"12f92404d9bddf211ec862f2da8d1e9e782deb430b3450d235eda8dc889e2cce","abstract_canon_sha256":"136aa86f7a059cd8d9f2b56a5d962f8b75a2672e2f844a40d2f4b34efc38f913"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:23.488667Z","signature_b64":"BJ4yH+CFhLK6l28nTkaLig2N+NM+VVc4UwGilhiE0Xp6lAuO+uaHiey/foD4OfZ/mJ1yhg/RIuqFpEyFIK26Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fc0487d2f3d7567e1e9d5ebab1d054591fcfa3941702bb1c1f7eb88ed1361d2","last_reissued_at":"2026-05-18T01:38:23.487944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:23.487944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A quadratic lower bound for subset sums","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bojan Mohar, Luis Goddyn, Matt DeVos, Robert Samal (Simon Fraser University)","submitted_at":"2006-12-02T04:20:48Z","abstract_excerpt":"Let A be a finite nonempty subset of an additive abelian group G, and let \\Sigma(A) denote the set of all group elements representable as a sum of some subset of A. 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