# Questions tagged [square-free]

An element of an integral domain is called *square-free* if it isn’t divisible by any non-unit square. Most notable applications are square-free integers and square-free polynomials.

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### Radicands of square roots of the 2020s, written in simplest radical form

As of the time of writing, the current decade is the 2020s. An interesting property of this decade is that there are 3 years that satisfy the property that the square-free part (https://oeis.org/...
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### Bounding a sum of reciprocals of square-free integers

(Cross-posted from MSE, as the question did not get any clear answer) Fix positive integers $k$ and $n$. Let $N_1,\dots,N_r$ be all the integers less than or equal to $n$ that are squarefree and have ...
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### Square-free numbers in an interval

Is there an explicit estimate in the literature bounding from above the number of square-free numbers in a short interval $x<n\leq x y$? I can easily do this by means of the Selberg sieve, but I do ...
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### Square-free Mersenne numbers

Questions about prime numbers are notoriously hard. Let me ask one which may be easier: QUESTION:  are there infinitely many square-free Mersenne numbers $$M(n)\ := 2^n-1$$ where $\ n\in\mathbb N\$ ...
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