Differential Transcendence of Solutions of the Difference Equation $$\Delta y=ay^2+by+c$$

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<jats:title>Abstract</jats:title><jats:p>By a purely algebraic way, we investigate a necessary and sufficient condition for the existence of differentially algebraic and transcendental solutions to certain difference equations whose form is related to Riccati equations. Our result roughly implies that all the solutions do not satisfy any algebraic differential equations if there is no algebraic solution.</jats:p>

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