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A010331
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Numbers that are expressible as C(m,5) + C(n,5) in at least 2 ways.
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0
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OFFSET
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1,1
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COMMENTS
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Did not find any other couple (m, n) with n <= m <= 600. - Michel Marcus, Feb 03 2014
No additional solutions with n <= m <= 25000 exist. Conjecture: no additional solutions exist. - Jon E. Schoenfield, Apr 13 2014
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LINKS
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EXAMPLE
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C(9,5) + C(9,5) = C(10,5) + C(4,5).
C(118,5) + C(117,5) = C(133,5) + C(78,5).
C(197,5) + C(160,5) = C(209,5) + C(53,5).
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PROG
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(PARI) findother(s, ma) = {forstep (i = ma-1, 4, -1, my(ci = binomial(i, 5)); if (2*ci < s, return([])); forstep (j = i, 4, -1, my(cj = binomial(j, 5)); if (ci+cj == s, return ([i, j])); ); ); return ([]); }
lista(ma, mb) = {for (m = ma, mb, my(cm = binomial(m, 5)); forstep (n = m, 4, -1, my(cn = binomial(n, 5)); my(s = cm+cn); vsol = findother(s, m); if (#vsol, print1(s, ", "); /*vsol = concat(vsol, [m, n]); print(vsol); */); ); ); } \\ Michel Marcus, Feb 03 2014
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CROSSREFS
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KEYWORD
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nonn,more,bref
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AUTHOR
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STATUS
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approved
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