Geodesic
On the equation $\varphi (|x^m-y^m|)=2^n$
Mathematica Bohemica, Tome 125 (2000) no. 4, pp. 465-479.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/MB.2000.126267
Classification : 11A25, 11A51, 11A63
Keywords: Euler function; Fermat primes 
@article{10_21136_MB_2000_126267,
     author = {Luca, Florian},
     title = {On the equation $\varphi (|x^m-y^m|)=2^n$},
     journal = {Mathematica Bohemica},
     pages = {465--479},
     publisher = {mathdoc},
     volume = {125},
     number = {4},
     year = {2000},
     doi = {10.21136/MB.2000.126267},
     mrnumber = {1802295},
     zbl = {0966.11002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2000.126267/}
}
TY  - JOUR
AU  - Luca, Florian
TI  - On the equation $\varphi (|x^m-y^m|)=2^n$
JO  - Mathematica Bohemica
PY  - 2000
SP  - 465
EP  - 479
VL  - 125
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2000.126267/
DO  - 10.21136/MB.2000.126267
LA  - en
ID  - 10_21136_MB_2000_126267
ER  - 
%0 Journal Article
%A Luca, Florian
%T On the equation $\varphi (|x^m-y^m|)=2^n$
%J Mathematica Bohemica
%D 2000
%P 465-479
%V 125
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2000.126267/
%R 10.21136/MB.2000.126267
%G en
%F 10_21136_MB_2000_126267
Luca, Florian. On the equation $\varphi (|x^m-y^m|)=2^n$. Mathematica Bohemica, Tome 125 (2000) no. 4, pp. 465-479. doi : 10.21136/MB.2000.126267. http://geodesic.mathdoc.fr/articles/10.21136/MB.2000.126267/

Cité par Sources :