PARTISI BILANGAN p(5n + 4); p(7n + 5) DAN p(11n + 6) SECARA BERTURUT-TURUT KONGRUEN MODULO 5, 7 DAN 11

Abstract

A partition of a positive integer is the representation of the positive integer its self or sums of the other positive integers, while the partition function is the number of partitions. This article disscusses a simple proof of partition numbers p(5n + 4), p(7n + 5) and p(11n + 6) consecutively congruent modulo 5, 7, and 11. The proof for modulo 5 and 7 are carried out via Jacobi identities, while for modulo 11 via Euler and Jacobi identities.