Special Prime Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 738    Accepted Submission(s): 390 Problem Description Give you a prime number p, if you could find some natural number (0 is not in…

题目链接: http://acm.hdu.edu.cn/showproblem.php?pid=2866 题目大意: 问你1到L中有多少个素数满足n^3 + p*n^2 = m^3(其中n,m为大于1的自然数) 解题思路: 首先简化成n^2 *( n + p ) = m^3 假设 n^2 和 n+p 之间有公共素因子 p , 那么 n+p = k*p , 即 n=p*(k-1), 带进去得到 p^3 * (k-1)^2 *k = m^3 , (k-1)^2*k 肯定是不能表示成某一个数的三次幂的…

题目网址:http://acm.hdu.edu.cn/showproblem.php?pid=2866 题意:在区间[2,L]内,有多少个素数p,满足方程有解. 分析: 原方程变为: n^(b-1) * (p+n) = m ^ b. 一开始,我们会想,这个方程在什么时候是有解的呢?? 肯定当左边式子能够凑成形如  X^b 这样的式子对不对?? 那么,也就是说,一定不存正整数k使得n = k*p. 即当且仅当gcd(n^(b-1),(p+n)) = 1时方程有解. 为什么?? 我们利用反证法可以进…

HDU 5839 Special Tetrahedron 题目链接http://acm.hdu.edu.cn/showproblem.php?pid=5839 Description Given n points which are in three-dimensional space(without repetition). Please find out how many distinct Special Tetrahedron among them. A tetrahedron is ca…

Problem hdu-2866 题意:求区间\([2,L]\)有多少素数\(p\)满足\(n^3+pn^2=m^3\),其中\(n,m\)属于任意整数 Solution 原式等价于\(n^2(p+n)=m^3\) 可证当\(p|\gcd(n^2,n+p)\)时,无解,因为当\(n=k\cdot p\)时 \(k^2p^3+k^3p^3=m^3\) \(m=p\sqrt [3]{k^2+k^3}\)可证无整数解,对于这一点,证明如下 \(k^2+k^3=k^2(1+k)\) 假如\(1+k\)为…

HDU 1005 Number Sequence(数论) Problem Description: A number sequence is defined as follows:f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7. Given A, B, and n, you are to calculate the value of f(n).   Input The input consists of multipl…

Least Common Multiple (HDU - 1019) [简单数论][LCM][欧几里得辗转相除法] 标签: 入门讲座题解 数论 题目描述 The least common multiple (LCM) of a set of positive integers is the smallest positive integer which is divisible by all the numbers in the set. For example, the LCM of 5, 7…

七夕节 (HDU - 1215) [简单数论][找因数] 标签: 入门讲座题解 数论 题目描述 七夕节那天,月老来到数字王国,他在城门上贴了一张告示,并且和数字王国的人们说:"你们想知道你们的另一半是谁吗?那就按照告示上的方法去找吧!" 人们纷纷来到告示前,都想知道谁才是自己的另一半.告示如下: 数字N的因子就是所有比N小又能被N整除的所有正整数,如12的因子有1,2,3,4,6. 你想知道你的另一半吗? Input 输入数据的第一行是一个数字T(1<=T<=500000)…

Special Prime Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 415    Accepted Submission(s): 220 Problem Description Give you a prime number p, if you could find some natural number (0 is not in…

Problem Description Let f(x) = anxn +...+ a1x +a0, in which ai (0 <= i <= n) are all known integers. We call f(x) 0 (mod m) congruence equation. If m is a composite, we can factor m into powers of primes and solve every such single equation after wh…