In computability theory, what are examples of decision problems of which it is not known whether they are [decidable](https://en.wikipedia.org/wiki/Undecidable_problem)?



Decision problems for which it is unknown whether they are decidable
An *integer linear recurrence sequence* is a sequence $x\_0, x\_1, x\_2, \ldots$ of integers that obeys a linear recurrence relation
$$x\_n = a\_1 x\_{n-1} + a\_2 x\_{n-2} + \cdots + a\_d x\_{n-d}$$
for some integer $d\ge 1$, some integer coefficients $a\_1, \ldots, a\_d$, and all $n\ge d$. The following problem is sometimes known as "Skolem's problem":



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> Given $d$, $a\_1, \ldots, a\_d$, $x\_0, \ldots x\_{d-1}$, does there exist $n$ such that $x\_n=0$ ?
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It is unknown whether the above problem is undecidable. For more information, see [Terry Tao's blog post](https://terrytao.wordpress.com/2007/05/25/open-question-effective-skolem-mahler-lech-theorem/) on the subject.


