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Using inequality techniques and coincidence degree theory, new results are provided concerning the existence and uniqueness of periodic solutions for the Duffing type p-Laplacian equation with multiple constant delays of the form (φp(x′(t)))′+Cx′(t)+g0(t,x(t))+∑k=1ngk(t,x(t-τk))=e(t). Moreover, an example is provided to illustrate the effectiveness of the results in this paper.