@article {FerrariSillari2023,
	title = {On the Minimal Number of Solutions of the Equation φ(n+k)=Mφ(n), M=1,2},
	journal = {Journal of Integer Sequences},
	volume = {26},
	year = {2023},
	month = {01/2023},
	type = {Article},
	abstract = {We fix a positive integer $k$ and look for solutions $n \in \mathbb{N}$ of the equations $\phi(n + k) = \phi(n)$ and $φ(n + k) = 2 φ(n)$. For $k \le 12 \cdot 10^{100}$, we prove that Fermat primes can be used to build five solutions for the first equation when $k$ is even, and five for the second one when $k$ is odd. Furthermore, for $k \le 4 \cdot 10^{58}$, we show that for the second equation there are at least three solutions when $k$ is even. Our work increases the previously known minimal number of solutions for both equations.},
	keywords = {Euler{\textquoteright}s phi function},
	issn = {1530-7638},
	url = {https://cs.uwaterloo.ca/journals/JIS/VOL26/Sillari/sillari3.html},
	author = {Matteo Ferrari and Lorenzo Sillari}
}
