数学趣题——验证四方定理
1、题目
所有自然数最多只要4个数的平方和就可以表示
2、源码
1: #include <stdio.h>
2: #include <math.h>
3:
4: int mode_1(int N) /*判断自然数N是否可以表示成为N=a2的形式*/
5: {
6: if((int)sqrt(N)*(int)sqrt(N)==N)
7: {
8: printf("%d*%d=%d\n",(int)sqrt(N),(int)sqrt(N),N);
9: return 1;
10: }
11: else return 0;
12: }
13:
14: int mode_2(int N) /*判断自然数N是否可以表示成N=a2+b2的形式*/
15: {
16: int x,y;
17: for(x=1;x<sqrt(N);x++)
18: for(y=x;y<sqrt(N);y++)
19: {
20: if(x*x+y*y == N)
21: {
22: printf("%d^2+%d^2=%d\n",x,y,N);
23: return 1;
24: }
25:
26: }
27: return 0;
28: }
29:
30: int mode_3(int N) /*判断自然数N是否可以表示成N=a2+b2+c2的形式*/
31: {
32: int x,y,z;
33: for(x=1;x<sqrt(N);x++)
34: for(y=x;y<sqrt(N);y++)
35: for(z=y;z<sqrt(N);z++)
36: {
37: if(x*x+y*y+z*z == N)
38: {
39: printf("%d^2+%d^2+%d^2=%d\n",x,y,z,N);
40: return 1;
41: }
42: }
43: return 0;
44: }
45:
46: int mode_4(int N) /*判断自然数N是否可以表示成N=a2+b2+c2+d2的形式*/
47: {
48: int x,y,z,t;
49: for(x=1;x<sqrt(N);x++)
50: for(y=x;y<sqrt(N);y++)
51: for(z=y;z<sqrt(N);z++)
52: for(t=z;t<sqrt(N);t++)
53: {
54: if(x*x+y*y+z*z+t*t == N)
55: {
56: printf("%d^2+%d^2+%d^2+%d^2=%d\n",x,y,z,t,N);
57: return 1;
58: }
59: }
60: return 0;
61: }
62:
63: void proveFourSquares(int N)
64: {
65: if(mode_1(N))
66: printf("It has verified Four Squares");
67: else if(mode_2(N))
68: printf("It has verified Four Squares");
69: else if(mode_3(N))
70: printf("It has verified Four Squares");
71: else if(mode_4(N))
72: printf("It has verified Four Squares");
73: }
74:
75: int main()
76: {
77: int N;
78: printf("Please input a natural number\n");
79: scanf("%d",&N);
80: printf("-------- Step of Verification---------\n");
81: proveFourSquares(N);
82: return 0;
83: }