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Ni, He-Xia; Pan, Hao
Journal of mathematical analysis and applications, 01/2020, Volume: 481, Issue: 2Journal Article
Z.-H. Sun (2014) proved a symmetric congruence∑k=0p−1(αk)(−1−αk)fk≡(−1)〈α〉p∑k=0p−1(αk)(−1−αk)fˆk(modp2), where p is an odd prime, α∈Q is p-integral, 〈α〉p is the least non-negative residue of α modulo p and fˆk=∑j=0k(−1)j(kj)fj. This congruence implies several supercongruences of Rodriguez-Villegas. In this paper, we give a q-analogue of this congruence and prove some symmetric q-congruences, which also confirm two conjectures of Guo and Zeng (2014).
