An elementary proof of a Rodriguez-Villegas supercongruence

2009/11/22 by Roberto Tauraso, Tauraso, Roberto · 1 citation
Mathematics · #05A10 #05A19 #11A07 #11B65 #Advanced Mathematical Identities #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:05A10 #msc:05A19 #msc:11A07 #msc:11B65

paper · pdf · doi:10.48550/arxiv.0911.4261

arxiv created 2009/11/22 · openalex publication_date 2009/11/22 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a short proof of the following known congruence: for every odd prime p ∑_k=0^p-12k\choose k² 16^-k≡ (-1)^{p-1\over 2}\pmodp². Moreover, we provide some new results connected with the above congruence.

Cited by

• Some q-analogues of (super)congruences of Beukers, Van Hamme and Rodriguez-Villegas

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