What is DifferenceRoot?

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In a question I asked earlier today in an effort to simplify the equation on the left below, I was pointed toward Wolfram Alpha.

I got this back:

Equation From Wolfram Alpha

I honestly have no idea what the right half of this is trying to say. From what I've gathered it has something to do with something called the linear distance equation. Please help.

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DifferenceRoot is simply a substitute for the solution to a difference equation.