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We establish the best (minimum) constant for Ulam stability of first-order linear hdifference equations with a periodic coefficient. First, we show Ulam stability and find the Ulam stability constant for a first-order linear equation with a period-two coefficient, and give several examples. In the last section we prove Ulam stability for a periodic coefficient function of arbitrary finite period. Results on the associated first-order perturbed linear equation with periodic coefficient are also included.2010 Mathematics Subject Classification. 39A10, 34N05, 39A23, 39A45.

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