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A267824
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Composite numbers n such that binomial(2n-1, n-1) == 1 (mod n^2).
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6
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OFFSET
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1,1
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COMMENTS
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Babbage proved the congruence holds if n > 2 is prime.
See A088164 and A263882 for references, links, and additional comments.
Conjecture: n is a term if and only if n = A088164(i)^2 for some i >= 1 (cf. McIntosh, 1995, p. 385). - Felix Fröhlich, Jan 27 2016
The "if" part of the conjecture is true: see the McIntosh reference. - Jonathan Sondow, Jan 28 2016
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LINKS
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EXAMPLE
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a(1) = 16843^2 and a(2) = 2124679^2 are squares of Wolstenholme primes A088164.
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CROSSREFS
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Cf. A000984, A034602, A082180, A088164, A099905, A099906, A099907, A099908, A136327, A177783, A212557, A228562, A242473, A244214, A244919, A246130, A246132, A246133, A246134, A260209, A260210, A263429, A263882, A281302.
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KEYWORD
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nonn,bref,hard,more
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AUTHOR
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STATUS
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approved
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