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- W4293225152 abstract "Let bt(n) count the number of t-regular partitions of n. In recent years, congruence properties of bt(n) have received a lot of attention and a number of infinite families of congruences modulo 2 for bt(n) have been proved for some small t. Very recently, Keith and Zanello investigated the parity of the coefficients of certain eta-quotients and proved new parity results for bt(n). In particular, they discovered new infinite families of congruences modulo 2 for b3(n) and those congruences involve every prime p with p ≡ 13,17,19, 23 (mod 24). Motivated by their work, we prove new infinite families of congruences modulo 2 for b3(n) and these congruences involve every prime p ≥ 5 based on Newman's results. Additionally, we proved new congruences for b3(n) which implies that there exist infinitely many positive integers m such that b3(m) is odd." @default.
- W4293225152 created "2022-08-27" @default.
- W4293225152 creator A5032007996 @default.
- W4293225152 date "2022-02-14" @default.
- W4293225152 modified "2023-09-30" @default.
- W4293225152 title "New parity results for 3-regular partitions" @default.
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- W4293225152 doi "https://doi.org/10.2989/16073606.2022.2033872" @default.
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