Arithmetic properties of 2-color overpartition pairs
M. S. M. Naika, S. S. Nayaka
Let pk,-2(n) counts the number of overpartition pairs of n with
2-color in which one of the colors appears only in parts
that are multiples of k. We establish several infinite families of congruences modulo powers of 2 and 3 for
pk,-2(n)
where k= 2 and 3. For example, for all n ≥ 0 and α ≥ 0,
we have
p2,-2(16 · 34α+2n + 34 · 34α+1) ≡ 0 (mod 128),
p3,-2(6 · 25α+2n + 20·25α+2) ≡ 0 (mod 27).
Tbilisi Mathematical Journal, Vol. 13(2) (2020), pp. 67-85
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