| № | Пользователь | Рейтинг |
|---|---|---|
| 1 | tourist | 4009 |
| 2 | jiangly | 3823 |
| 3 | Benq | 3738 |
| 4 | Radewoosh | 3633 |
| 5 | jqdai0815 | 3620 |
| 6 | orzdevinwang | 3529 |
| 7 | ecnerwala | 3446 |
| 8 | Um_nik | 3396 |
| 9 | ksun48 | 3390 |
| 10 | gamegame | 3386 |
| Страны | Города | Организации | Всё → |
| № | Пользователь | Вклад |
|---|---|---|
| 1 | cry | 167 |
| 2 | Um_nik | 163 |
| 3 | maomao90 | 162 |
| 3 | atcoder_official | 162 |
| 5 | adamant | 159 |
| 6 | -is-this-fft- | 158 |
| 7 | awoo | 157 |
| 8 | TheScrasse | 154 |
| 9 | Dominater069 | 153 |
| 9 | nor | 153 |
giving n positive integers a1,a2,...,an. gcd(a1,a2,...,an)=1. define f(x1,x2,...,xn)=a1*x1+a2*x2+a3*x3+...+an*xn(xi>=0). what is the maximum number b that can not be expressed by f(x1,x2,...,xn)? x1,x2,...,xn are all non-negative integers.
I already know the answer for n=2, it's equal to a1*a2-a1-a2. but when n>2,I can't get it. can anyone give me some hints?
It seems that if gcd(a1,a2...,an)=1 then you can express every number, don't you?
No. For example, min(a1,a2,...,an)-1 can't be expressed.
Oh, now I see that all values xi must be non-negative, you're right.
No polynomial solution is known for this problem. Read this Wikipedia page for more information.
thanks, I first known this problem in the book "A Friendly Introduction to Number Theory", it ask you to solve with the situation n=2. When I work it out and try to solve with n=3, I find it's quite another one. That's really a pity that this problem can't be described by a beautiful formula or algorithm.