Lin, Hsueh-Yung Odd Catalan numbers modulo \(2^k\). (English) Zbl 1251.11010 Integers 12, No. 2, 161-165 (2012); 11, A55, 5 p. (2011). Summary: This article proves a conjecture by S.-C. Liu and J. C.-C. Yeh [J. Integer Seq. 13, No. 5, Article ID 10.5.4, 26 p. (2010; Zbl 1230.05013)] about Catalan numbers, which states that odd Catalan numbers can take exactly \(k-1\) distinct values modulo \(2^k\), namely the values \(C_{2^1-1},\dots, C_{2^{k-1}-1}\). Cited in 1 ReviewCited in 1 Document MSC: 11B65 Binomial coefficients; factorials; \(q\)-identities 11A07 Congruences; primitive roots; residue systems Keywords:odd Catalan numbers Citations:Zbl 1230.05013 PDFBibTeX XMLCite \textit{H.-Y. Lin}, Integers 12, No. 2, 161--165 (2012; Zbl 1251.11010) Full Text: DOI arXiv EMIS Online Encyclopedia of Integer Sequences: Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).