General and Recursive Forms of Catalan Numbers and Modulo Prime Catalan Numbers to the Power of Positive Integers

Authors

  • agus sugandha Universitas Jenderal Soedirman
  • Irfan Azkamahendra

DOI:

https://doi.org/10.54199/pjse.v2i2.133

Keywords:

Catalan numbers, combinations, congruences, prime numbers, modulo

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

Published

2022-08-23

Issue

Section

Artikel