Scholarlink

<p>Various <i>q</i>-congruences related to Carlitz’s formula have been recently studied by many authors. We establish a unified form of these <i>q</i>-congruences, which includes all of the known <i>q</i>-congruences motivated by Carlitz’s formula as special cases. Apart from Carlitz’s formula and a <i>q</i>-analogue of Morley’s congruence, important ingredients in our proof of the unified form include a <i>q</i>-analogue of Granville’s congruence and a recurrence formula for a summation. As an application, we prove a <i>q</i>-congruence conjectured by Tauraso.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

q-Supercongruences Motivated by Carlitz’s Formula

  • 期刊论文

  • 发表日期：

    2025年6月23日

查看全文
  • Ji-Cai Liu,
  • Jing Liu

摘要

Various q-congruences related to Carlitz’s formula have been recently studied by many authors. We establish a unified form of these q-congruences, which includes all of the known q-congruences motivated by Carlitz’s formula as special cases. Apart from Carlitz’s formula and a q-analogue of Morley’s congruence, important ingredients in our proof of the unified form include a q-analogue of Granville’s congruence and a recurrence formula for a summation. As an application, we prove a q-congruence conjectured by Tauraso.