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The analogous statement for families of k k-nomial coefficients (k>1) was conjectured in 1997 by David Wasserman.\n  Erd\\H{o}s and Szekeres remark that if m_1, m_2, n_1, n_2 as above are all >1, there is probably a lower bound on the common divisor in question which goes to infinity as a function of m_1+m_2. Such a bound is here obtained.\n  Results are proved that narrow the class of possible"},"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":"0806.0607","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-06-03T18:37:01Z","cross_cats_sorted":[],"title_canon_sha256":"00248588223e5a2415ec1808eb34dff61bffbcdce6cee358ae9237f4d31ab138","abstract_canon_sha256":"760827c07ef4da3dc1d21b2d794c9f46559225f765f8d934c4d7b44302bc1359"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:10.767197Z","signature_b64":"x+itIzzyIt5Nyo+WAbm9ZQx3uSI3aptsVyhfdql8PKaOuJVrpWnS+bi0Wz3imU82l9Jy2di03lA56nQIgYNIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d670380dd381f7fbab00008a0b75e361a68ca74c7aae2a256aa4769067e9af73","last_reissued_at":"2026-05-18T03:26:10.766511Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:10.766511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On common divisors of multinomial coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"George M. Bergman","submitted_at":"2008-06-03T18:37:01Z","abstract_excerpt":"Erd\\H{o}s and Szekeres showed in 1978 that for any four positive integers satisfying m_1+m_2 = n_1+n_2, the two binomial coefficients (m_1+m_2)!/m_1! m_2! and (n_1+n_2)!/n_1! n_2! have a common divisor >1. The analogous statement for families of k k-nomial coefficients (k>1) was conjectured in 1997 by David Wasserman.\n  Erd\\H{o}s and Szekeres remark that if m_1, m_2, n_1, n_2 as above are all >1, there is probably a lower bound on the common divisor in question which goes to infinity as a function of m_1+m_2. 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