A Proof of Merca's Conjectures on Sums of Odd Divisor Functions

15 Jul 2021 · Kaya Lakein, Anne Larsen ·

In a recent paper, Merca posed three conjectures on congruences for specific convolutions of a sum of odd divisor functions with a generating function for generalized $m$-gonal numbers. Extending Merca's work, we complete the proof of these conjectures.