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Let {En} be the Euler numbers. In the paper we determine E2mk+b − Eb modulo 2m+7, where k,m are positive integers with m 4 and b 2 {0, 2, 4, . . . }.
If w = u for ∈ = {1, 2} and u ∈ ∗, then w is said to be a simple right extension of u and denoted by u ≺ w. Let k be a positive integer and Pk(") denote the set of all C∞-words of he...