given an array consists of $$$n$$$ integers and an integer $$$p$$$, find number of pair($$$i,j$$$):
so that $$$i<j$$$ and $$$(a[i]*a[j])$$$ $$$mod$$$ $$$p$$$ $$$=$$$ $$$(a[i]+a[j])$$$ $$$mod$$$ $$$p$$$
$$$n<=10^5$$$
$$$1<p<=10^9$$$
№ | Пользователь | Рейтинг |
---|---|---|
1 | tourist | 3845 |
2 | jiangly | 3707 |
3 | Benq | 3630 |
4 | orzdevinwang | 3573 |
5 | Geothermal | 3569 |
5 | cnnfls_csy | 3569 |
7 | jqdai0815 | 3532 |
8 | ecnerwala | 3501 |
9 | gyh20 | 3447 |
10 | Rebelz | 3409 |
Страны | Города | Организации | Всё → |
№ | Пользователь | Вклад |
---|---|---|
1 | maomao90 | 171 |
2 | adamant | 163 |
3 | awoo | 162 |
4 | maroonrk | 152 |
4 | nor | 152 |
6 | -is-this-fft- | 151 |
7 | TheScrasse | 148 |
8 | atcoder_official | 146 |
9 | Petr | 145 |
10 | pajenegod | 144 |
given an array consists of $$$n$$$ integers and an integer $$$p$$$, find number of pair($$$i,j$$$):
so that $$$i<j$$$ and $$$(a[i]*a[j])$$$ $$$mod$$$ $$$p$$$ $$$=$$$ $$$(a[i]+a[j])$$$ $$$mod$$$ $$$p$$$
$$$n<=10^5$$$
$$$1<p<=10^9$$$
Название |
---|
Im not sure if this really works, but this is what I thought: rearranging the expression, we have $$$a_i \cdot a_j - (a_i+a_j) \equiv 0 \mod{p}$$$, which is equivalent to $$$(a_i-1)(a_j-1) \equiv 1 \mod{p}.$$$ This implies that $$$a_i \equiv a_j \equiv 0$$$ or $$$2 \mod{p}$$$. Then, let $$$x$$$ be the number of $$$a_k$$$ such that $$$a_k \equiv 0 \mod{p}$$$ and $$$y$$$ the number of $$$a_l$$$ such that $$$a_l \equiv 2 \mod{p}$$$. Answer is $$${x \choose 2} + {y \choose 2}$$$.
actually, this is not correct. You can pair every $$$a_i$$$ with any $$$a_j \equiv (a_i-1)^{-1}+1 \mod{p}$$$.
please give the problem link
http://online.vku.udn.vn/problem/tongtich
you can translate it into english