The well-known Catalan numbers, studied for nearly two centuries, are named after the Belgian mathematician E. C. Catalan. Around 1883, he established that the number X_(a,b) = (2a)! (2b)! / a! b! (a b)! , where a, b ≥ 0, is an integer. This article focuses on applications of this number-theoretic fact to Catalan numbers, including some divisibility properties.
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