A positive integer n is called E-symmetric if there exists a positive integer m such that |m-n| = (ϕ(m),ϕ(n)), and n is called E-asymmetric if it is not E-symmetric. We show that there are infinitely many E-symmetric and E-asymmetric primes.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-3,
author = {Gang Yu},
title = {E-symmetric numbers},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {17-25},
zbl = {1078.11005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-3}
}
Gang Yu. E-symmetric numbers. Colloquium Mathematicae, Tome 103 (2005) pp. 17-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-3/