1樓:匿名使用者
證明:假設奇數:
2n+1
那麼任意三個奇數:
2*i + 1
2*j + 1
2*k + 1
相加等於
2(i + j + k) + 3
少年你還說這種問題有解嗎
再不相信:
1+1+1 = 3
1+1+3 = 5
1+1+5 = 7
1+1+7 = 9
1+1+9 = 11
1+1+11 = 13
1+1+13 = 15
1+1+15 = 17
1+3+1 = 5
1+3+3 = 7
1+3+5 = 9
1+3+7 = 11
1+3+9 = 13
1+3+11 = 15
1+3+13 = 17
1+3+15 = 19
1+5+1 = 7
1+5+3 = 9
1+5+5 = 11
1+5+7 = 13
1+5+9 = 15
1+5+11 = 17
1+5+13 = 19
1+5+15 = 21
1+7+1 = 9
1+7+3 = 11
1+7+5 = 13
1+7+7 = 15
1+7+9 = 17
1+7+11 = 19
1+7+13 = 21
1+7+15 = 23
1+9+1 = 11
1+9+3 = 13
1+9+5 = 15
1+9+7 = 17
1+9+9 = 19
1+9+11 = 21
1+9+13 = 23
1+9+15 = 25
1+11+1 = 13
1+11+3 = 15
1+11+5 = 17
1+11+7 = 19
1+11+9 = 21
1+11+11 = 23
1+11+13 = 25
1+11+15 = 27
1+13+1 = 15
1+13+3 = 17
1+13+5 = 19
1+13+7 = 21
1+13+9 = 23
1+13+11 = 25
1+13+13 = 27
1+13+15 = 29
1+15+1 = 17
1+15+3 = 19
1+15+5 = 21
1+15+7 = 23
1+15+9 = 25
1+15+11 = 27
1+15+13 = 29
1+15+15 = 31
3+1+1 = 5
3+1+3 = 7
3+1+5 = 9
3+1+7 = 11
3+1+9 = 13
3+1+11 = 15
3+1+13 = 17
3+1+15 = 19
3+3+1 = 7
3+3+3 = 9
3+3+5 = 11
3+3+7 = 13
3+3+9 = 15
3+3+11 = 17
3+3+13 = 19
3+3+15 = 21
3+5+1 = 9
3+5+3 = 11
3+5+5 = 13
3+5+7 = 15
3+5+9 = 17
3+5+11 = 19
3+5+13 = 21
3+5+15 = 23
3+7+1 = 11
3+7+3 = 13
3+7+5 = 15
3+7+7 = 17
3+7+9 = 19
3+7+11 = 21
3+7+13 = 23
3+7+15 = 25
3+9+1 = 13
3+9+3 = 15
3+9+5 = 17
3+9+7 = 19
3+9+9 = 21
3+9+11 = 23
3+9+13 = 25
3+9+15 = 27
3+11+1 = 15
3+11+3 = 17
3+11+5 = 19
3+11+7 = 21
3+11+9 = 23
3+11+11 = 25
3+11+13 = 27
3+11+15 = 29
3+13+1 = 17
3+13+3 = 19
3+13+5 = 21
3+13+7 = 23
3+13+9 = 25
3+13+11 = 27
3+13+13 = 29
3+13+15 = 31
3+15+1 = 19
3+15+3 = 21
3+15+5 = 23
3+15+7 = 25
3+15+9 = 27
3+15+11 = 29
3+15+13 = 31
3+15+15 = 33
5+1+1 = 7
5+1+3 = 9
5+1+5 = 11
5+1+7 = 13
5+1+9 = 15
5+1+11 = 17
5+1+13 = 19
5+1+15 = 21
5+3+1 = 9
5+3+3 = 11
5+3+5 = 13
5+3+7 = 15
5+3+9 = 17
5+3+11 = 19
5+3+13 = 21
5+3+15 = 23
5+5+1 = 11
5+5+3 = 13
5+5+5 = 15
5+5+7 = 17
5+5+9 = 19
5+5+11 = 21
5+5+13 = 23
5+5+15 = 25
5+7+1 = 13
5+7+3 = 15
5+7+5 = 17
5+7+7 = 19
5+7+9 = 21
5+7+11 = 23
5+7+13 = 25
5+7+15 = 27
5+9+1 = 15
5+9+3 = 17
5+9+5 = 19
5+9+7 = 21
5+9+9 = 23
5+9+11 = 25
5+9+13 = 27
5+9+15 = 29
5+11+1 = 17
5+11+3 = 19
5+11+5 = 21
5+11+7 = 23
5+11+9 = 25
5+11+11 = 27
5+11+13 = 29
5+11+15 = 31
5+13+1 = 19
5+13+3 = 21
5+13+5 = 23
5+13+7 = 25
5+13+9 = 27
5+13+11 = 29
5+13+13 = 31
5+13+15 = 33
5+15+1 = 21
5+15+3 = 23
5+15+5 = 25
5+15+7 = 27
5+15+9 = 29
5+15+11 = 31
5+15+13 = 33
5+15+15 = 35
7+1+1 = 9
7+1+3 = 11
7+1+5 = 13
7+1+7 = 15
7+1+9 = 17
7+1+11 = 19
7+1+13 = 21
7+1+15 = 23
7+3+1 = 11
7+3+3 = 13
7+3+5 = 15
7+3+7 = 17
7+3+9 = 19
7+3+11 = 21
7+3+13 = 23
7+3+15 = 25
7+5+1 = 13
7+5+3 = 15
7+5+5 = 17
7+5+7 = 19
7+5+9 = 21
7+5+11 = 23
7+5+13 = 25
7+5+15 = 27
7+7+1 = 15
7+7+3 = 17
7+7+5 = 19
7+7+7 = 21
7+7+9 = 23
7+7+11 = 25
7+7+13 = 27
7+7+15 = 29
7+9+1 = 17
7+9+3 = 19
7+9+5 = 21
7+9+7 = 23
7+9+9 = 25
7+9+11 = 27
7+9+13 = 29
7+9+15 = 31
7+11+1 = 19
7+11+3 = 21
7+11+5 = 23
7+11+7 = 25
7+11+9 = 27
7+11+11 = 29
7+11+13 = 31
7+11+15 = 33
7+13+1 = 21
7+13+3 = 23
7+13+5 = 25
7+13+7 = 27
7+13+9 = 29
7+13+11 = 31
7+13+13 = 33
7+13+15 = 35
7+15+1 = 23
7+15+3 = 25
7+15+5 = 27
7+15+7 = 29
7+15+9 = 31
7+15+11 = 33
7+15+13 = 35
7+15+15 = 37
9+1+1 = 11
9+1+3 = 13
9+1+5 = 15
9+1+7 = 17
9+1+9 = 19
9+1+11 = 21
9+1+13 = 23
9+1+15 = 25
9+3+1 = 13
9+3+3 = 15
9+3+5 = 17
9+3+7 = 19
9+3+9 = 21
9+3+11 = 23
9+3+13 = 25
9+3+15 = 27
9+5+1 = 15
9+5+3 = 17
9+5+5 = 19
9+5+7 = 21
9+5+9 = 23
9+5+11 = 25
9+5+13 = 27
9+5+15 = 29
9+7+1 = 17
9+7+3 = 19
9+7+5 = 21
9+7+7 = 23
9+7+9 = 25
9+7+11 = 27
9+7+13 = 29
9+7+15 = 31
9+9+1 = 19
9+9+3 = 21
9+9+5 = 23
9+9+7 = 25
9+9+9 = 27
9+9+11 = 29
9+9+13 = 31
9+9+15 = 33
9+11+1 = 21
9+11+3 = 23
9+11+5 = 25
9+11+7 = 27
9+11+9 = 29
9+11+11 = 31
9+11+13 = 33
9+11+15 = 35
9+13+1 = 23
9+13+3 = 25
9+13+5 = 27
9+13+7 = 29
9+13+9 = 31
9+13+11 = 33
9+13+13 = 35
9+13+15 = 37
9+15+1 = 25
9+15+3 = 27
9+15+5 = 29
9+15+7 = 31
9+15+9 = 33
9+15+11 = 35
9+15+13 = 37
9+15+15 = 39
11+1+1 = 13
11+1+3 = 15
11+1+5 = 17
11+1+7 = 19
11+1+9 = 21
11+1+11 = 23
11+1+13 = 25
11+1+15 = 27
11+3+1 = 15
11+3+3 = 17
11+3+5 = 19
11+3+7 = 21
11+3+9 = 23
11+3+11 = 25
11+3+13 = 27
11+3+15 = 29
11+5+1 = 17
11+5+3 = 19
11+5+5 = 21
11+5+7 = 23
11+5+9 = 25
11+5+11 = 27
11+5+13 = 29
11+5+15 = 31
11+7+1 = 19
11+7+3 = 21
11+7+5 = 23
11+7+7 = 25
11+7+9 = 27
11+7+11 = 29
11+7+13 = 31
11+7+15 = 33
11+9+1 = 21
11+9+3 = 23
11+9+5 = 25
11+9+7 = 27
11+9+9 = 29
11+9+11 = 31
11+9+13 = 33
11+9+15 = 35
11+11+1 = 23
11+11+3 = 25
11+11+5 = 27
11+11+7 = 29
11+11+9 = 31
11+11+11 = 33
11+11+13 = 35
11+11+15 = 37
11+13+1 = 25
11+13+3 = 27
11+13+5 = 29
11+13+7 = 31
11+13+9 = 33
11+13+11 = 35
11+13+13 = 37
11+13+15 = 39
11+15+1 = 27
11+15+3 = 29
11+15+5 = 31
11+15+7 = 33
11+15+9 = 35
11+15+11 = 37
11+15+13 = 39
11+15+15 = 41
13+1+1 = 15
13+1+3 = 17
13+1+5 = 19
13+1+7 = 21
13+1+9 = 23
13+1+11 = 25
13+1+13 = 27
13+1+15 = 29
13+3+1 = 17
13+3+3 = 19
13+3+5 = 21
13+3+7 = 23
13+3+9 = 25
13+3+11 = 27
13+3+13 = 29
13+3+15 = 31
13+5+1 = 19
13+5+3 = 21
13+5+5 = 23
13+5+7 = 25
13+5+9 = 27
13+5+11 = 29
13+5+13 = 31
13+5+15 = 33
13+7+1 = 21
13+7+3 = 23
13+7+5 = 25
13+7+7 = 27
13+7+9 = 29
13+7+11 = 31
13+7+13 = 33
13+7+15 = 35
13+9+1 = 23
13+9+3 = 25
13+9+5 = 27
13+9+7 = 29
13+9+9 = 31
13+9+11 = 33
13+9+13 = 35
13+9+15 = 37
13+11+1 = 25
13+11+3 = 27
13+11+5 = 29
13+11+7 = 31
13+11+9 = 33
13+11+11 = 35
13+11+13 = 37
13+11+15 = 39
13+13+1 = 27
13+13+3 = 29
13+13+5 = 31
13+13+7 = 33
13+13+9 = 35
13+13+11 = 37
13+13+13 = 39
13+13+15 = 41
13+15+1 = 29
13+15+3 = 31
13+15+5 = 33
13+15+7 = 35
13+15+9 = 37
13+15+11 = 39
13+15+13 = 41
13+15+15 = 43
15+1+1 = 17
15+1+3 = 19
15+1+5 = 21
15+1+7 = 23
15+1+9 = 25
15+1+11 = 27
15+1+13 = 29
15+1+15 = 31
15+3+1 = 19
15+3+3 = 21
15+3+5 = 23
15+3+7 = 25
15+3+9 = 27
15+3+11 = 29
15+3+13 = 31
15+3+15 = 33
15+5+1 = 21
15+5+3 = 23
15+5+5 = 25
15+5+7 = 27
15+5+9 = 29
15+5+11 = 31
15+5+13 = 33
15+5+15 = 35
15+7+1 = 23
15+7+3 = 25
15+7+5 = 27
15+7+7 = 29
15+7+9 = 31
15+7+11 = 33
15+7+13 = 35
15+7+15 = 37
15+9+1 = 25
15+9+3 = 27
15+9+5 = 29
15+9+7 = 31
15+9+9 = 33
15+9+11 = 35
15+9+13 = 37
15+9+15 = 39
15+11+1 = 27
15+11+3 = 29
15+11+5 = 31
15+11+7 = 33
15+11+9 = 35
15+11+11 = 37
15+11+13 = 39
15+11+15 = 41
15+13+1 = 29
15+13+3 = 31
15+13+5 = 33
15+13+7 = 35
15+13+9 = 37
15+13+11 = 39
15+13+13 = 41
15+13+15 = 43
15+15+1 = 31
15+15+3 = 33
15+15+5 = 35
15+15+7 = 37
15+15+9 = 39
15+15+11 = 41
15+15+13 = 43
15+15+15 = 45
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