# Questions tagged [number-theory]

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

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### Compute the Carmichael function

Task description In number theory, the Carmichael function λ takes a positive integer n and returns the least positive integer k so that the k-th power of each integer coprime to n equals 1 modulo n. ...
314 views

### Misconstrued Monomials

There exists an equation, assuming n and x are positive, that expresses the relationship between two monomials, one being a ...
543 views

### Constructible n-gons

A constructible $n$-gon is a regular polygon with n sides that you can construct with only a compass and an unmarked ruler. As stated by Gauss, the only $n$ for which a $n$-gon is constructible ...
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### Is this a Smith number?

Challenge description A Smith number is a composite number whose sum of digits is equal to the sum of sums of digits of its prime factors. Given an integer N, ...
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### Excessive Integers

For a positive integer n with the prime factorization n = p1^e1 * p2^e2 * ... pk^ek where ...
690 views

### Score Tarzan's Olympic Vine-Swinging Routine

Olympic vine-swingers perform their routines in standard trees. In particular, Standard Tree n has vertices for 0 up through <...
188 views

### Compute the polyomino capacity of a rectangle

Write a program or function that takes as input three positive integers x, y, and a and ...
395 views

### Dense Number Sequence

OEIS: A167171 A dense number is a number that has exactly as many prime divisors as non-prime divisors (including 1 and itself as divisors). Equivalently, it is either a prime or a product of two ...
538 views

### Smallest positive integer which is coprime to the last two predecessors and has not yet appeared; a(1)=1, a(2)=2

Definition Two integers are coprime if they share no positive common divisors other than 1. a(1) = 1 ...
169 views

In this challenge we'll compute an infinite minimal admissible sequence. The sequence for this challenge starts with a(1) = 1. We continue this sequence by ...
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Executive summary: test whether an input sequence of integers is "admissible", meaning that it doesn't cover all residue classes for any modulus. What is an "admissible" sequence? Given an integer m ...
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### Numbers of purity

Today we'll look at a sequence $a$, related to the Collatz function $f$: f = \begin{cases} n/2 & \text{if } n \equiv 0 \text{ (mod }2) \\ 3n+1 & \text{if } n \equiv 1 \text{ (mod }2) \\ ...
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### Is it a Proth number?

A Proth number, named after François Proth, is a number that can be expressed as N = k * 2^n + 1 Where k is an odd positive ...
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