Let $g(n)$ count the number of $m$ such that $\varphi (m)=n$. Is it true that, for every $ϵ>0$, there exist infinitely many $n$ such that$$g(n)>n^{1-ϵ}?$$

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

If we write (A(n):=|\\{m:\varphi(m)=n\\}|), then your (g(n)=A(n)). What you are asking is whether

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.