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Let denote the th cyclotomic polynomial in . Recently, Guo, Schlosser and Zudilin proved that for any integer with ,
where . In this note, we give a generalization of the above -congruence to the modulus case. Meanwhile, we give a corresponding -congruence modulo for . Our proof is based on the ‘creative microscoping’ method, recently developed by Guo and Zudilin, and a summation formula.
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