I was skimming again through Dummit & Foote's Abstract Algebra and I came across this exercise:
Prove that for any given positive integer $N$ there exist only finitely many integers $n$ with $\varphi(n)=N$, where $\varphi$ denotes Euler $\varphi$-function. Conclude in particular that $\varphi(n)$ tends to infinity as $n$ tends to infinity.
I don't doubt that $\varphi(n) \to \infty$ as $n \to \infty$. However, if I recall Erdös proved that if there is an $x_0$ such that $\varphi(x_0)=N$, then there must be infinitely many integers such that $\varphi(x)=N$. See this article for a mention of this (it's in the very first $2$ lines).
Am I reading something wrong here? Has has Dummit and Foote actually asked the impossible? Or does the MathWorld site contain an error?