2002 IMO 第 3 题

N3 (MON) Let $p_{1}, p_{2}, \ldots, p_{n}$ be distinct primes greater than 3 . Show that $2^{p_{1} p_{2} \cdots p_{n}}+1$ has at least $4^{n}$ divisors.

N3 (MON) 令 $p_{1}, p_{2}, \ldots, p_{n}$ 为大于 3 的不同素数。证明 $2^{p_{1} p_{2} \cdots p_{n}}+1$ 至少有 $4^{n}$ 个约数。