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Note on a discrete initial value problem from a competition
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DOI：10.1186/s13662-021-03251-w.png)
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Abstract
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The following discrete initial value problem xn+1=xn(xn-12-2)-x1,n is an element of N,x0=2 and x1=5/2, appeared at an international competition. It is known that the problem can be solved in closed form. Here we discuss the solvability of a more general initial value problem which includes the former one. We show that, in a sense, there are not so many solvable discrete initial value problems related to this one, showing its specificity, which is a bit surprising result.
Keywords:
Discrete initial value problem
Nonlinear difference equation
Closed-form formula
Solvable equation
39A20
39A06
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