Conjectural overpartition congruence modulo 19

For a positive integer nn, let p(n)\overline{p}(n) denote the number of overpartitions of nn, and let (np)\left(\frac{n}{p}\right) denote the Legendre symbol for an odd prime pp. Congruence modulo 19.

p(1724n)0(mod19),\overline{p}(17^2\cdot 4n)\equiv 0\pmod{19},

where n3(mod8)n\equiv 3\pmod 8, (n17)=1\left(\frac{n}{17}\right)=-1, and (n19)=1\left(\frac{n}{19}\right)=1. It involves 7272 residue classes modulo 25842584, which the source does not list. The source presents this as another conjectural Ramanujan-type congruence that cannot be proved by the methods in the paper; no resolution is supplied.

Sources & referencesView supporting material

Primary source

XuanLing Wei, “New Ramanujan-type congruences for overpartitions modulo 11 and 13”, arXiv:2603.08510 (2026).

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