Sums and differences of power-free numbers

Julia Brandes. "Sums and differences of power-free numbers." Acta Arithmetica 169.2 (2015): 169-180. <http://eudml.org/doc/278927>.

@article{JuliaBrandes2015,
abstract = {We employ a generalised version of Heath-Brown's square sieve in order to establish an asymptotic estimate of the number of solutions a, b ∈ ℕ to the equations a + b = n and a - b = n, where a is k-free and b is l-free. This is the first time that this problem has been studied with distinct powers k and l.},
author = {Julia Brandes},
journal = {Acta Arithmetica},
keywords = {power-free numbers; power sieve},
language = {eng},
number = {2},
pages = {169-180},
title = {Sums and differences of power-free numbers},
url = {http://eudml.org/doc/278927},
volume = {169},
year = {2015},
}

TY - JOUR
AU - Julia Brandes
TI - Sums and differences of power-free numbers
JO - Acta Arithmetica
PY - 2015
VL - 169
IS - 2
SP - 169
EP - 180
AB - We employ a generalised version of Heath-Brown's square sieve in order to establish an asymptotic estimate of the number of solutions a, b ∈ ℕ to the equations a + b = n and a - b = n, where a is k-free and b is l-free. This is the first time that this problem has been studied with distinct powers k and l.
LA - eng
KW - power-free numbers; power sieve
UR - http://eudml.org/doc/278927
ER -