Questions tagged [number-theory]
Number theory involves properties and relationships of numbers, primarily positive integers.
479 questions
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Draw the Gauss Star (Heptadecagram)
Background
In 1796, 18-year-old Carl Friedrich Gauss proved that a regular heptadecagon can be constructed with compass and straightedge — the first such discovery in over 2,000 years. The stonemason ...
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Golf a number bigger than all other answers [duplicate]
You have to code in python, and the number generated by your code must be bigger than all other current submissions. You need to make your code as small as possible, it has to terminate but you can ...
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IMO 2025: Divisor sums that go forever
Problem 4 of the 2025 International Mathematical Olympiad asked (paraphrased):
Let \$f(n)\$ be the sum of the largest three proper divisors of \$n\$,
that is divisors excluding \$n\$ itself. For ...
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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 ...
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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 ...
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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 ...
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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 ...
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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
$...
- 1,742
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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\$ ...
- 3,898
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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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