# Questions tagged [number-theory]

Number theory involves properties and relationships of numbers, primarily positive integers.

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### Golfing the complexity with subtraction

The Mahler-Popken complexity, $C(N)$, of a positive integer, $N$, is the smallest number of ones ($1$) that can be used to form $N$ in a mathematical expression using only the integer* $1$ ...
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### *Trivial* near-repdigit perfect powers

Task Output the sequence that precisely consists of the following integers in increasing order: the 2nd and higher powers of 10 ($10^i$ where $i \ge 2$), the squares of powers of 10 times 2 or 3 (...
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### Output a 1-2-3-5-7... sequence

Follow-up of my previous challenge, inspired by @emanresu A's question, and proven possible by @att (Mathematica solution linked) For the purposes of this challenge, a 1-2-3-5-7... sequence is an ...
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### Output a 1-2-3 sequence

For the purposes of this challenge, a 1-2-3 sequence is an infinite sequence of increasing positive integers such that for any positive integer $n$, exactly one of $n, 2n,$ and $3n$ appears in ...
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### Pretty Palintiples

Imagine you have a positive integer number $n$. Let $m$ be the number obtained by reversing $n$'s digits. If $m$ is a whole multiple of $n$, then $n$ is said to be a reverse divisible ...
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### Is it a tetrate of two?

The tetration operation consists of repeated exponentiation, and it is written ↑↑. For instance, 3↑↑3 =3 ^(3^3) = 3^27 = 7,625,597,484,987 A tetrate of two is an ...
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