2022/07/18 by CHUANAN WEI, Chuanan Wei
Mathematics · Computer Science · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Polynomial and algebraic computation
paper · doi:10.1017/s0004972722000636
Abstract We derive a q -supercongruence modulo the third power of a cyclotomic polynomial with the help of Guo and Zudilin’s method of creative microscoping [‘A q -microscope for supercongruences’, Adv. Math. 346 (2019), 329–358] and the q -Dixon formula. As consequences, we give several supercongruences including \beginalign*∑k=0(p-2)/3(((2)/(3))k3)/((1)k3)≡(p)/(2)\frac(1)(p-2)/3((4)/(3))(p-2)/3\pmodp3,\endalign* where p is a prime with p≡ 5\pmod 6 .