Das–Nath–Sarma congruences for generalized Frobenius partitions

The problem concerns congruences conjectured by Das, Nath, and Sarma in 2026 for generalized Frobenius partitions. The claimed result targets the two progressions modulo $16$ specified in those conjectures.

September 10, 2026 claimed proof

On September 10, 2026, Manjil P. Saikia's preprint Generalized Frobenius Partitions Modulo Powers of $2$ claimed a general congruence for $k$-colored generalized Frobenius partitions: for every $m\geq 2$ and $k\equiv 2\pmod{2^m}$. At $k=18$ and modulus $16$, it claims to prove

$$c\phi_{18}(30n+19)\equiv c\phi_{18}(30n+25)\equiv 0\pmod{16}.$$

It also claims further modulo-$16$ congruences and a modulo-$8$ characterization. No independent verification, error report, or withdrawal was found.

Current status (as of September 2026): The two Das–Nath–Sarma congruences are claimed proved by Saikia's preprint, but the proof remains unverified; the additional claimed congruences are likewise unconfirmed.