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.