LAUSR

Abstract In this paper, via the WZ method and the summation package Sigma , we establish the following two supercongruences: ∑ k = 0 ( p + 1 ) / 2 ( 3 k − 1 ) ( − 1 2 ) k 2 ( 1 2 ) k 4 k k ! 3 ≡ p − 6 p 3 ( − 1 p ) + 2 p 3 ( − 1 p ) E p − 3 ( mod p 4 ) , ∑ k = 0 p − 1 ( 3 k − 1 ) ( − 1 2 ) k 2 ( 1 2 ) k 4 k k ! 3 ≡ p − 2 p 3 ( mod p 4 ) , where p > 3 is a prime, E p − 3 is the ( p − 3 ) -th Euler number and ( − 1 p ) = ( − 1 ) ( p − 1 ) / 2 is the Legendre symbol. The first congruence modulo p 3 confirms a recent conjecture of Guo and Schlosser.