On the equation $\varphi \left(\right|x^m-y^m\left|\right)=2^n$

Luca, Florian. "On the equation $\varphi (|x^m-y^m|)=2^n$." Mathematica Bohemica 125.4 (2000): 465-479. <http://eudml.org/doc/248665>.

@article{Luca2000,
abstract = {In this paper we investigate the solutions of the equation in the title, where $\phi $ is the Euler function. We first show that it suffices to find the solutions of the above equation when $m=4$ and $x$ and $y$ are coprime positive integers. For this last equation, we show that aside from a few small solutions, all the others are in a one-to-one correspondence with the Fermat primes.},
author = {Luca, Florian},
journal = {Mathematica Bohemica},
keywords = {Euler function; Fermat primes; Euler function; Fermat primes},
language = {eng},
number = {4},
pages = {465-479},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the equation $\varphi (|x^m-y^m|)=2^n$},
url = {http://eudml.org/doc/248665},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Luca, Florian
TI - On the equation $\varphi (|x^m-y^m|)=2^n$
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 4
SP - 465
EP - 479
AB - In this paper we investigate the solutions of the equation in the title, where $\phi $ is the Euler function. We first show that it suffices to find the solutions of the above equation when $m=4$ and $x$ and $y$ are coprime positive integers. For this last equation, we show that aside from a few small solutions, all the others are in a one-to-one correspondence with the Fermat primes.
LA - eng
KW - Euler function; Fermat primes; Euler function; Fermat primes
UR - http://eudml.org/doc/248665
ER -