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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-2-4,
author = {Julia Brandes},
title = {Sums and differences of power-free numbers},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {169-180},
zbl = {06446122},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-2-4}
}
Julia Brandes. Sums and differences of power-free numbers. Acta Arithmetica, Tome 168 (2015) pp. 169-180. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa169-2-4/