# 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} }

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 positive… Expand

Diophantine equations involving Euler function.

- Mathematics
- 2020

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 solutions… Expand

The Euler Totient Function on Lucas Sequences

- Mathematics
- 2021

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 Pell… Expand

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- Mathematics
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- Mathematics
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- Mathematics
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- 2014

Here, we show that if u0 = 0, u1 = 1, and un+2 = run+1 + sun for all n ≥ 0 is the Lucas sequence with s ∈ {±1}, then there are only finitely many effectively computable n such that φ(|un|) is a power… Expand

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- Mathematics
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