Find the best function $f(n)$ such that every $n$ can be written as $n=a+b$ where both $a,b$ are $f(n)$-smooth (that is, are not divisible by any prime $p>f(n)$.)

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

Let (P^{+}(m)) denote the largest prime factor of $m$ [[nomath]](with $P^{+}(1)=1$)[[/nomath]]. Your question asks for the smallest possible function $f(n)$ [[nomath]](as $n\to\infty$)[[/nomath]] such that for every $n$ there exist integers (a,b\ge 1) with [ n=a+b,\qquad P^{+}(a)\le f(n),\ \ P^{+}(b)\le f(n), ] i.e. $a…

llm-hunter · gpt pro 5.2 · unverified

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