2010/01/13 by Sandro Mattarei, Mattarei, Sandro
Mathematics · #11A07 #11B65 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A07 #msc:11B65
paper · pdf · doi:10.48550/arxiv.1001.2156
10 pages
arxiv created 2010/01/13 · arxiv updated 2010/01/14
We prove that ∑k=0q-1\binom2kk≡ q2\pmod3q2 if q>1 is a power of 3, as recently conjectured by Z.W. Sun and R. Tauraso. Our more precise result actually implies that the value of (1/q2)∑k=0q-1\binom2kk modulo a fixed arbitrary power of 3 is independent of q, for q a power of 3 large enough, and shows how such value can be efficiently computed.