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We study the flavor-changing-neutral-current process c → uμ+μ- using 1.3 fb-1 of pp collisions at √s = 1.96 TeV recorded by the D0 detector operating at the Fermilab Tevatron Collider. We see clear indications of the charged-current mediated D+s and D+ → φπ+ → μ+μ-π+ final states with significance greater than 4 standard deviations above background for the D+ state. We search for the continuum neutral-current decay of D+ → μ+μ-π+ in the dimuon invariant mass spectrum away from the φ resonance. We see no evidence of signal above background and set a limit of B(D+ → π+μ+μ-) < 3.9 x 10-6 at the 90% C.L. This limit places the most stringent constraint on new phenomena in the c → uμ+μ- transition.