Computational proofs of congruences for 2-colored Frobenius partitions

In 1994, the following infinite family of congruences was conjectured for the partition functioncΦ2(n)which counts the number of2-colored Frobenius partitions ofn: for alln≥0andα≥1,cΦ2(5αn+λα)≡0(mod5α), whereλαis the least positive reciprocal of12modulo5α. In this paper, the first four cases of this family are proved.