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MathNet 2022-part-03 — 197 problems (EN–VI) Question 55

Math Olympiad Vault · MathNet 2022-part-03 — 197 problems (EN–VI)

Question 55

Let $a_{1}=1$ and, for every $n \geq 2$,
$$
a_{n}=n\left(a_{1}+a_{2}+\cdots+a_{n-1}\right) .
$$
What is the smallest value of $n$ for which $a_{n}$ is divisible by 2022?
(A) 47
(B) 289
(C) 337
(D) 2022
(E) 2023