# Congruences modulo powers of 5 for three-colored Frobenius partitions

@article{Xiong2010CongruencesMP, title={Congruences modulo powers of 5 for three-colored Frobenius partitions}, author={X. Xiong}, journal={arXiv: Number Theory}, year={2010} }

Motivated by a question of Lovejoy \cite{lovejoy}, we show that three-colored Frobenius partition function $\c3$ and related arithmetic fuction $\cc3$ vanish modulo some powers of 5 in certain arithmetic progressions.

## 6 Citations

Congruences for generalized Frobenius partitions with 4 colors

- Computer Science, MathematicsDiscret. Math.
- 2011

We present some congruences involving the functions [email protected]"4(n) and [email protected]@?"4(n) which denote, respectively, the number of generalized Frobenius partitions of n with 4 colors…

An Unexpected Congruence Modulo 5 for 4--Colored Generalized Frobenius Partitions

- Mathematics
- 2013

In his 1984 AMS Memoir, George Andrews defined the family of $k$--colored generalized Frobenius partition functions. These are denoted by $c\phi_k(n)$ where $k\geq 1$ is the number of colors in…

Infinitely many congruences modulo 5 for 4-colored Frobenius partitions

- Mathematics
- 2016

In his 1984 AMS Memoir, Andrews introduced the family of functions $$c\phi _k(n),$$cϕk(n), which denotes the number of generalized Frobenius partitions of $$n$$n into $$k$$k colors. Recently, Baruah…

Congruences for Generalized Frobenius Partitions with an Arbitrarily Large Number of Colors

- Computer Science, MathematicsIntegers
- 2014

Several infinite families of congruences for $c\phi_k(n)$ where $k$ is allowed to grow arbitrarily large are proved, relying on a generating function representation which appears in Andrews' Memoir but has gone relatively unnoticed.

Congruence properties for a certain kind of partition functions

- Mathematics
- 2016

In light of the modular equations of fifth and seventh order, we derive some congruence properties for a certain kind of partition functions a(n) which satisfy ∑n=0∞a(n)qn≡(q;q)∞k(modm), where k is a…

Generalized Frobenius partitions with 6 colors

- Mathematics
- 2015

We present the generating function for $$c\phi _6(n)$$cϕ6(n), the number of generalized Frobenius partitions of $$n$$n with $$6$$6 colors, in terms of Ramanujan’s theta functions and exhibit $$2$$2,…

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