ANALISIS FAKTOR YANG MEMPENGARUHI KEMISKINAN DI KABUPATEN BANYUMASBENTUK UMUM DAN REKURSIF BILANGAN CATALAN SERTA BILANGAN CATALAN MODULO PRIMA BERPANGKAT BILANGAN BULAT POSITIF

Abstract

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