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Newest 'number-theory' Questions - Code Golf Stack Exchange
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Learn more about TeamsQuestions tagged [number-theory]
Number theory involves properties and relationships of numbers, primarily positive integers.
476 questions
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23
votes
6
answers
2k
views
Computing Pi with iF*ck
Objective
Compute \$\pi\$ using nothing but \$i\$ (\$\sqrt{-1}\$).
Guidelines
ONLY exponentiation and multiplication may be used (i.e. \$i^i\$ or \$ii\$)
No additional symbols may be used (so no ...
8
votes
17
answers
4k
views
Is this number Ugly?
Related, but not dupe (Asking about the n-th k-smooth number whereas I'm only asking if a certain number is 5-smooth.)Source: Partially inspired by Leetcode's 5-smooth Number problem, but partially ...
20
votes
28
answers
3k
views
Is the number sum of 3 squares?
Challenge
Write a program (function) that given a nonnegative integer input, output whether the number can be represented as the sum of 3 square numbers. That is, the program should, given nonnegative ...
11
votes
7
answers
2k
views
Perfect ruler search
Definitions:
A sparse ruler, or simply a ruler, is a strict increasing finite sequence of nonnegative integers starting from 0, called marks.
A ruler is complete if the set of all distances it can ...
11
votes
13
answers
983
views
Number of complete binary unordered tree-factorizations of n
For prime p, the factorization tree is a single vertex in just one way so that a(p) = 1.
For composite n, the two subtrees at n are a split of n into two factors n = d * (n/d), without order, so that
$...
14
votes
5
answers
668
views
Sum-of-four-squares grid
Output a grid of characters visualizing the decomposition of a number into a sum of four perfect squares.
Challenge
Given a nonnegative integer \$0 \le n \le 2^{30}\$, output a \$2^k \times 2^k\$ ...
16
votes
6
answers
1k
views
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\$ ...
14
votes
13
answers
931
views
*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 (...
11
votes
4
answers
2k
views
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 ...
22
votes
15
answers
2k
views
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 ...
15
votes
16
answers
1k
views
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 ...
18
votes
26
answers
2k
views
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 ...
11
votes
10
answers
2k
views
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} < \...
4
votes
5
answers
460
views
Generate a sequence of \$n\$ consecutive composite numbers
Definitions
The common methods to generate consecutive composites are
$$\overbrace{(n+1)! + 2, \ (n+1)! + 3, \ \ldots, \ (n+1)! + (n+1)}^{\text{n composites}}$$
$$\overbrace{n!+2,n!+3,...,n!+n}^{\text{...
13
votes
20
answers
1k
views
Modular Equivalence
Given two numbers \$x,y > 2, x≠y \$ output all integers \$m\$ such that
$$
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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