[en] The production of K⁺ and π⁺ mesons and protons in pBe collisions at T_p=2.9 GeV has been studied at the ITEP proton synchrotron. Ejectiles with a momentum of p=545 MeV/c were observed under an emission angle θ=17 . The detectors which have been developed for the identification of kaons out of a six orders of magnitude more intense background of pions and protons are described. A cross-section ratio d²σ_K⁺/dΩdp:d²σ_π⁺/dΩdp:d²σ_p/dΩdp of (1±0.34):(85±1):(31±1) has been measured. Normalization with existing pion data yields an invariant differential cross section E.d³σ_K⁺/d³p=(3.1±1.2) mb GeV^-2 c³ sr^-1 and a total cross section of σ_tot(pBe)=(3.7±1.5) mb. These cross sections are compared with existing data and theoretical predictions. The A dependence of K⁺ production in the few-GeV range is analyzed. (orig.)