FU’S p α DOTS BRACELET PARTITION

Abstract

This paper aims to explore the arithmetic properties of Fu’s k dots bracelet partition where k = p^α, p is a prime number with p ≥ 5 and α is an integer with α ≥ 0. For p^α dots bracelet partitions with p = 5, 7 and 11, we found several exciting Ramanujan-like congruences modulo p. We also used Newman’s theorems to demonstrate certain congruence modulo p.