# Number Theory Seminar

Tuesday, September 17, 2019 — 1:30 PM EDT

J.C. Saunders, Ben Gurion University of Negev

"Diophantine equations involving the Euler totient function"

We deal with various Diophantine equations involving the Euler totient function. In particular, for $a,b,c,m,n\in\mathbb{N}$ with $m\geq 2$ we study the equations $\varphi(ax^m)=\frac{b\cdot n!}{c}$ and $\varphi\left(\frac{b\cdot n!}{c}\right)=ax^m$ where $\varphi(x)$ is the Euler totient function. We also deal with similar equations involving Lucas sequences of the first kind and second kind, generalising the work of Luca and Stanica.

MC 5417

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