General and Recursive Forms of Catalan Numbers and Modulo Prime Catalan Numbers to the Power of Positive Integers
Keywords:Catalan numbers, combinations, congruences, prime numbers, modulo
. A Catalan number is a positive number obtained by calculating the combined structure of a sequence. Catalan numbers have a general form and a recursive form that can be identified through Diagonal-Avoiding Paths and Balanced Parentheses. Catalan numbers have congruence on the modulo of integers. One of them is on the prime number modulo p. For every odd prime p, p does not divisible by and the product of all numbers d by d between 0 and and the Greatest Common Divisor of d and p is 1, will be congruent to -1 modulo . For every integer a with a between 0 and , the Catalan numbers have different values on modulo and is congruent to and so on until modulo . For a between (p+1) to p , the catalan numbers have different values on modulo and is congruent to and so on until modulo .
Keywords: Catalan numbers, combinations, congruences, prime numbers, modulo
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