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 ...
- 2,093
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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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Egyptian fraction representations of 1 without prime denominators
Background
As noted in this question, for all positive integers \$n>2\$ there exists at least one Egyptian fraction representation (EFR) of \$n\$ distinct positive integers \$a_{1} < a_{2} < \...
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Generate a sequence of \$n\$ consecutive composite numbers
Definitions
The common methods to generate consecutive composites are
$$\overbrace{(n+1)! + 2, \ (n+1)! + 3, \ \ldots, \ (n+1)! + (n+1)}^{\text{n composites}}$$
$$\overbrace{n!+2,n!+3,...,n!+n}^{\text{...
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Modular Equivalence
Given two numbers \$x,y > 2, x≠y \$ output all integers \$m\$ such that
$$
x + y \equiv x \cdot y \pmod m
$$
$$
x \cdot y > m > 2
$$
Input
Two integers
Output
A list of integers
Test cases
<...
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Make 1's and 2's composite
Input
An integer k composed of 1 and 2, with at least 3 digits and at most 200 digits.
...
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Consecutive Composite Numbers
Challenge
Generate \$n-1\$ consecutive composite numbers using this prime gap formula
$$n!+2,n!+3,...,n!+n$$
Input
An integer \$n\$ such that \$3 \leq n \leq 50 \$.
Output
Sequence of \$n-1\$ ...
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17
votes
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Ellipse Lattice Point Counter
Challenge
Determine how many integer lattice points there are in an ellipse
$$\frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1$$
centered at the origin with width \$2a\$ and height \$2b\$ where integers \$a, ...
- 2,211
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votes
2
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Construct this point
Given a constructible point \$(x, y) \in \mathbb R^2\$, output the steps required to construct \$(x, y)\$
Constructing a point
Consider the following "construction" of a point \$(\alpha, \...
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Visualise the Euclidean GCD [duplicate]
The Euclidean GCD Algorithm is an algorithm that efficiently computes the GCD of two positive integers, by repeatedly subtracting the smaller number from the larger number until they become equal. It ...
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Random factorized numbers
Input
The code should take an integer \$n\$ between 1 and 1000.
Output
The code should output positive integers with \$n\$ bits. Accompanying each integer should be its full factorization. Each ...
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