Computational proofs of congruences for 2‐colored Frobenius partitions

In 1994, the following infinite family of congruences was conjectured for the partition function c Φ 2 ( n ) which counts the number of 2‐colored Frobenius partitions of n : for all n ≥ 0 and α ≥ 1, c Φ 2 (5 α n + λ α ) ≡ 0(mod5 α ), where λ α is the least positive reciprocal of 12 modulo 5 α . In this paper, the first four cases of this family are proved.