# Questions tagged [number-theory]

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

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### Sum of two squares

Given a nonnegative integer $n$, determine whether $n$ can be expressed as the sum of two square numbers, that is $\exists a,b\in\mathbb Z$ such that $n=a^2+b^2$. ...
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### Egyptian fraction representations of 1

An Egyptian fraction is a representation of a rational number using the sum of distinct unit fractions (a unit fraction is of the form $\frac 1 x$ where $x$ is a positive integer). For all[1] ...
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### High throughput prime numbers

This challenge is inspired by the High throughput Fizz Buzz challenge. The goal Generate a list of prime numbers up to 10,000,000,000,000,000. The output of primes should be in decimal digits followed ...
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### Write the most optimized assembly program to detect a prime number (from a bigger range!)

This is the second version of the task. The original task had a defect that the given range of integers was too small. This was pointed out by @harold that other methods couldn't defeat the way of ...
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### Order of an algebraic number

Consider some arbitrary polynomial with integer coefficients, $$a_n x^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0 = 0$$ We'll assume that $a_n \ne 0$ and $a_0 \ne 0$. The solutions to this polynomial ...
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### AoCG2021 Day 24: Is the bus company cheating?

Part of Advent of Code Golf 2021 event. See the linked meta post for details. Related to AoC2020 Day 13, Part 2. Why Bubbler isn't posting this; Why Riker isn't posting this A shuttle bus service ...
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### Count occurrences in Pascal's Triangle

Pascal's triangle is a triangular diagram where the values of two numbers added together produce the one below them. This is the start of it: ...
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### Is it a row of Pascal's triangle?

Pascal's triangle is a triangular diagram where the values of two numbers added together produce the one below them. This is the start of it: ...
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### Euler's numerus idoneus

Euler's numerus idoneus, or idoneal numbers, are a finite set of numbers whose exact number is unknown, as it depends on whether or not the Generalized Riemann hypothesis holds or not. If it does, ...
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### How many iterations to reach the sequence?

Let's define a function $f$ which, given a positive integer $x$, returns the sum of: $x$ the smallest digit in the decimal representation of $x$ the highest digit in the decimal ...
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