The Auluck-Chowla-Gupta conjecture asserts that, for every positive integer 
, the numbers of partitions of
into exactly 
parts form a unimodal sequence
as 
ranges from 1 to 
. Writing these numbers as 
, the sequence is 
.
Padhi (2026) proved the conjecture for every 
, combining an analytic argument for 
with exact finite verification through 
. This completes Szekeres's sufficiently-large-
result (Szekeres 1953). The sequence need not be log-concave.
Padhi (2026) reports using Claude for computations and code and takes responsibility for the proof and its reproducible computational claims.
