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Everything about Square-free integer
Number without repeated prime factors
In mathematics, a square-free integer (or squarefree integer) is an integer that is divisible by no square number other than 1. That is, its prime factorization has exactly one factor for each prime that appears in it. For example, 10 = 2 ⋅ 5 is square-free, but 18 = 2 ⋅ 3 ⋅ 3 is not, because 18 is divisible by 9 = 32. The smallest positive square-free numbers are Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Square-free integerA 5-minute orientation
- Skim a recent paper: Every integer can be written as a square plus a squarefreeInfluential work since 2022
- Pick up a classic book: The mathematics of Paul ErdösThe most-reprinted book on the subject
- Read the landmark paper: An Efficient Exact Quantum Algorithm for the Integer Square-free Decomposition ProblemCited 17 times
- Go sideways: Composite numberA closely related topic
- Go sideways: Greatest common divisorA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
An Efficient Exact Quantum Algorithm for the Integer Square-free Decomposition Problem
The Representation of an Integer as the Sum of the Square of a Prime and of a Square-Free Integer
A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator
Factorization of Integer-Valued Polynomials with Square-Free Denominator
Cubic one-regular graphs of order twice a square-free integer
The Factors of a Square-Free Integer
On the representation of the integer by positive quadratic forms with square-free variables
On symmetric graphs of order four times an odd square-free integer and valency seven
🆕 Influential since 2022
Every integer can be written as a square plus a squarefree
Arc-Transitive Graphs of Valency 11 and Order Four Times an Odd Square-free Integer
Fast square-free decomposition of integers using class groups
Square-free and square-full part of an integer
Counting Integer Matrices with Square-Free Determinants
📚 Books worth reading
The mathematics of Paul ErdösRonald L. Graham, Jaroslav Nešetřil · 1997
Coding the MatrixPhilip N. Klein · 2013- 📕The number of unitary, square-free divisors of an integer I-IID. Suryanarayana · 1969
Using Concurrency and Parallelism Effectively – IJon Kerridge · 2013
Using Concurrency and Parallelism Effectively – IJon Kerridge · 2013
Using Concurrency and Parallelism Effectively – IJon Kerridge · 2013
Using Concurrency and Parallelism Effectively – I (2nd edition)Jon Kerridge · 2015
Using Concurrency and Parallelism Effectively – II (2nd edition)Jon Kerridge · 2015
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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