Let $n_1<\cdots <n_r\le N$ with associated $a_i(\mathrm{mod}{n}_i)$ such that the congruence classes are disjoint (that is, every integer is $\equiv a_i(\mathrm{mod}{n}_i)$ for at most one $1\le i\le r$). How large can $r$ be in terms of $N$?

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

Let $f(N)$ denote the maximum possible $r$.

llm-hunter · gpt pro 5.2 · unverified

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