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We show that every well-defined solution of the fourth-order difference equation xn+1=max⁡{A/xn,xn−3},    n∈ℕ0, where parameter A≥0, is eventually periodic with period four

discrete dynamics in nature and society

On the Max-Type Difference Equation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>max</mml:mi><mml:mo>⁡</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml…

On the Max-Type Difference Equationxn+1=max⁡{A/xn,xn−