We deal with a linear differential equation with piecewise constant argument. The considered equation with the initial condition has the unique solution. We obtain the sufficient conditions for existence of n-periodic solution for the considered problem and describe the positivity conditions for the solution. KEYWORDS partial differential equation, piecewise constant arguments, periodic solution, asymptotically stable ACKNOWLEDGEMENTS Authors were partially supported by [grant number FZ-20200929224] of Fundamental Science Foundation of Uzbekistan. Authors thank the referee for valuable comments and gratefully acknowledge. FOR CITATION Muminov M.I., Radjabov T.A. On existence conditions for periodic solutions to a differential equation with constant argument.