HMMT 二月 2001 · 冲刺赛 · 第 60 题
HMMT February 2001 — Guts Round — Problem 60
题目详情
英文原题
- [ ∞ ] Find an n such that n ! − ( n − 1)! + ( n − 2)! − ( n − 3)! + · · · ± 1! is prime. Be
{
n, n ≤ 25
prepared to justify your answer for points, where [ N ] is the greatest integern +225
, n> 25
[ ]
less than N .10
解析
英文解析
- [ ∞ ] Find an n such that n ! − ( n − 1)! + ( n − 2)! − ( n − 3)! + · · · ± 1! is prime. Be
{
n, n ≤ 25
prepared to justify your answer for points, where [ N ] is the greatest integern +225
, n> 25
[ ]
less than N .10
Solution: 3, 4, 5, 6, 7, 8, 10, 15, 19, 41 (26 points), 59, 61 (28 points), 105 (33 points),
160 (38 points) are the only ones less than or equal to 335. If anyone produces an answerlarger than 335, then we ask for justification to call their bluff. It is not known whether ornot there are infinitely many such n . 9