# Diophantine equations involving the Euler totient function

@article{Saunders2019DiophantineEI,
title={Diophantine equations involving the Euler totient function},
author={J. C. Saunders},
journal={arXiv: Number Theory},
year={2019}
}
• J. C. Saunders
• Published 5 February 2019
• Mathematics
• arXiv: Number Theory
We deal with various Diophantine equations involving the Euler totient function and various sequences of numbers, including factorials, powers, and Fibonacci sequences.
3 Citations
On Fixed Points of Iterations Between the Order of Appearance and the Euler Totient Function
• Mathematics
• 2020
Let Fn be the nth Fibonacci number. The order of appearance z(n) of a natural number n is defined as the smallest positive integer k such that Fk≡0(modn). In this paper, we shall find all positiveExpand
Diophantine equations involving Euler function.
In this paper, we show that the equation $\varphi(|x^{m}-y^{m}|)=|x^{n}-y^{n}|$ has no nontrivial solutions in integers $x,y,m,n$ with $xy\neq0, m>0, n>0$ except for the solutionsExpand
The Euler Totient Function on Lucas Sequences
In 2009, Luca and Nicolae [14] proved that the only Fibonacci numbers whose Euler totient function is another Fibonacci number are 1, 2, and 3. In 2015, Faye and Luca [7] proved that the only PellExpand

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