【三角形数量】

cathetus（直角边）； hypotenuse（斜边）

spoj：Structures

     给定三角形的直角边，问可以有多少种三角形。 T<=10 , N<=1e15 ，times<=1s.

spoj：Shared cathetus (easy)

     给定三角形的直角边，问可以有多少种三角形。T<=1e5，N<=1e9，times<=1.899s.

spoj：Pythagorean Triple Counting1

    给定三角形的直角边，问可以有多少种三角形。T<=1e3，N<=1e15，times<=30s.

spoj：Pythagorean Triple Counting2

给定三角形的直角边，问可以有多少种三角形。T<=1e3，N<=1e15，times<=1s.

 

spoj：Pythagorean triples (medium)

给出N；（N<1.2e8），问有多少个三角形的斜边小于等于N。tiems:1s-15s

spoj：Counting Pythagorean Triples

给出N；（N<1.2e12），问有多少个三角形的斜边小于等于N。tiems:1s-15s

ZOJ1574：Pythagorean Triples

 求第N个prim直角三角形（即a和b互素）。按a，b的优先度关键字排序。N<1e5。

 

EIJ127:Pythagorean triples

 求第N直角三角形，按c，a，b的优先关键字排序。N<1e6。

 

CIRCIRC - Missing Side

 给出三角形两边，求第三边。使得这个三角形的外接三角形面积减内接三角形面积最小。

codeforces 707 C： Pythagorean Triples

给定三角形一条边（直角边或斜边），输出其他两条边。T=1，N<=1e9；

          当a>1，为奇数, 令x=(a-1)/2; b=2*x*(x+1),c=2*x*(x+1)+1; 
          当a>2，为偶数，令x=a/2;  b=x*x-1,c=x*x+1; 

#include<bits/stdc++.h>
#define ll long long
using namespace std;
int main()
{
    ll N,x,b,c;
    scanf("%lld",&N);
    if(N==1||N==2) printf("-1
");
    else {
        x=N/2;
        if(N&1LL) b=2*x*(x+1),c=b+1;
        else b=x*x-1,c=b+2;
        printf("%lld %lld
",b,c); 
    }
    return 0;
}

There are 16 primitive Pythagorean triples with c ≤ 100:

(3, 4, 5)	(5, 12, 13)	(8, 15, 17)	(7, 24, 25)
(20, 21, 29)	(12, 35, 37)	(9, 40, 41)	(28, 45, 53)
(11, 60, 61)	(16, 63, 65)	(33, 56, 65)	(48, 55, 73)
(13, 84, 85)	(36, 77, 85)	(39, 80, 89)	(65, 72, 97)

Note, for example, that (6, 8, 10) is not a primitive Pythagorean triple, as it is a multiple of (3, 4, 5). Each of these low-c points forms one of the more easily recognizable radiating lines in the scatter plot.

Additionally these are all the primitive Pythagorean triples with 100 < c ≤ 300:

(20, 99, 101)	(60, 91, 109)	(15, 112, 113)	(44, 117, 125)
(88, 105, 137)	(17, 144, 145)	(24, 143, 145)	(51, 140, 149)
(85, 132, 157)	(119, 120, 169)	(52, 165, 173)	(19, 180, 181)
(57, 176, 185)	(104, 153, 185)	(95, 168, 193)	(28, 195, 197)
(84, 187, 205)	(133, 156, 205)	(21, 220, 221)	(140, 171, 221)
(60, 221, 229)	(105, 208, 233)	(120, 209, 241)	(32, 255, 257)
(23, 264, 265)	(96, 247, 265)	(69, 260, 269)	(115, 252, 277)
(160, 231, 281)	(161, 240, 289)	(68, 285, 293)

【参考】维基百科：https://en.wikipedia.org/wiki/Pythagorean_triple