a 2 + b 2 = c 2 (a, b, c) a 2 a 2 = a a a 1/ 78
2/ 78
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4/ 78
180 5/ 78
http://www.kaijo.ed.jp/ 6/ 78
a, b, c ABC C a b B c A C 90 a 2 + b 2 = c 2 7/ 78
C a b a 2 +b 2 = c 2 B c A a 2 a a 2 = a a 8/ 78
C a b a 2 +b 2 = c 2 B c A a 2 a a 2 = a a 9/ 78
a C b a 2 + b 2 = c 2 B c A 10/ 78
a 2 a C b a 2 + b 2 = c 2 B c A 11/ 78
a 2 a C b b 2 a 2 + b 2 = c 2 B c A c 2 12/ 78
a 2 a C b b 2 a 2 + b 2 = c 2 B c A C c 2 a 2 + b 2 = c 2 13/ 78
2500 14/ 78
a 2 + b 2 = c 2 (a, b, c) (a, b, c) 15/ 78
(3, 4, 5) 3 2 + 4 2 = 9 + 16 = 25 = 5 2 (5, 12, 13) 5 2 + 12 2 = 25 + 144 = 169 = 13 2 (8, 15, 17) 8 2 + 15 2 = 64 + 225 = 289 = 17 2 (7, 24, 25) 7 2 + 24 2 = 49 + 576 = 625 = 25 2 16/ 78
(3, 4, 5) 3 2 + 4 2 = 9 + 16 = 25 = 5 2 (5, 12, 13) 5 2 + 12 2 = 25 + 144 = 169 = 13 2 (8, 15, 17) 8 2 + 15 2 = 64 + 225 = 289 = 17 2 (7, 24, 25) 7 2 + 24 2 = 49 + 576 = 625 = 25 2 17/ 78
(6, 8, 10) 6 2 + 8 2 = 36 + 64 = 100 = 10 2 (9, 12, 15) 9 2 + 12 2 = 81 + 144 = 225 = 15 2 (12, 16, 20) 12 2 + 16 2 = 144 + 256 = 400 = 20 2 (15, 20, 25) 15 2 + 20 2 = 225 + 400 = 625 = 25 2 (3, 4, 5) 18/ 78
(6, 8, 10) 6 2 + 8 2 = 36 + 64 = 100 = 10 2 (9, 12, 15) 9 2 + 12 2 = 81 + 144 = 225 = 15 2 (12, 16, 20) 12 2 + 16 2 = 144 + 256 = 400 = 20 2 (15, 20, 25) 15 2 + 20 2 = 225 + 400 = 625 = 25 2 (3, 4, 5) 19/ 78
a 2 + b 2 = c 2 a, b, c 3 5 4 5 12 13 6 8 10 9 c 12 15 20/ 78
(6, 8, 10) (9, 12, 15) (3, 4, 5) 3 4 5 6 8 10 9 (a, b, c) 1 12 15 21/ 78
1 22/ 78
2 3 1 2 4 2 2 3 4 1 23/ 78
24/ 78
m n m n (a, b, c) a = m 2 n 2, b = 2 m n, c = m 2 + n 2 25/ 78
a = m 2 n 2 m n b = 2 m n c = m 2 + n 2 n = 1 m = 2 (3, 4, 5) m = 3 m n m = 4 (15, 8, 17) a = 2 2 1 2 = 3, b = 2 2 1 = 4, c = 2 2 + 1 2 = 5
a = m 2 n 2 m n b = 2 m n c = m 2 + n 2 n = 1 m = 2 (3, 4, 5) m = 3 m n m = 4 (15, 8, 17)
a = m 2 n 2 m n b = 2 m n c = m 2 + n 2 n = 1 m = 2 (3, 4, 5) m = 3 m n m = 4 (15, 8, 17) a = 4 2 1 2 = 15, b = 2 4 1 = 8, c = 4 2 + 1 2 = 17
m n 10 m n a b c 2 1 3 4 5 4. 1. 15. 8. 17. 29/ 78
m n a b c 2 1 3 4 5 4 1 15 8 17 6 1 35 12 37 8 1 63 16 65 10 1 99 20 101 3 2 5 12 13 5 2 21 20 29 7 2 45 28 53 m n a b c 9 2 77 36 85 4 3 7 24 25 8 3 55 48 73 10 3 91 60 109 5 4 9 40 41 7 4 33 56 65 9 4 65 72 97 m n a b c 6 5 11 60 61 8 5 39 80 89 7 6 13 84 85 8 7 15 112 113 10 7 51 140 149 9 8 17 144 145 10 9 19 180 181 22 30/ 78
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c a r r b 35/ 78
5 3, 4, 5 3 r r 4 36/ 78
3 r 5 3 r 4 r 3 r r 4 r 5 = (3 r) + (4 r) r 1 4 37/ 78
a r c a r r b b r 38/ 78
a b c r 3 4 5 1 15 8 17 3 35 12 37 5 63 16 65 7 99 20 101 9 5 12 13 2 21 20 29 6 a b c r 77 36 85 14 7 24 25 3 55 48 73 15 91 60 109 21 9 40 41 4 33 56 65 12 65 72 97 20 a b c r 11 60 61 5 39 80 89 15 13 84 85 6 15 112 113 7 51 140 149 21 17 144 145 8 19 180 181 9 45 28 53 10 39/ 78
a a r r r c c = (a r) + (b r) r b r r = a + b c 2 a, b, c a + b c r b 40/ 78
a a r r r c c = (a r) + (b r) r b r r = a + b c 2 a, b, c a + b c r b 41/ 78
42/ 78
a b 2 a b c 3, 4, 5 3 4 = 6 2 43/ 78
a b 2 4 3 5 3, 4, 5 3 4 = 6 2 44/ 78
a c b 45/ 78
a b a b a b 3 4 6 15 8 60 35 12 210 63 16 504 99 20 990 5 12 30 21 20 210 77 36 1386 7 24 84 55 48 1320 91 60 2730 9 40 180 33 56 924 65 72 2340 11 60 330 39 80 1560 13 84 546 15 112 840 51 140 3570 17 144 1224 19 180 1710 45 28 630 6 46/ 78
6 a b 2 a c a b m n a = m 2 n 2 b = 2 m n b m n 47/ 78
6 ( ) = a b 2 = (m2 n 2 ) 2 m n 2 = (m 2 n 2 ) m n m 2 n 2 = (m + n) (m n) ( ) = (m + n) (m n) m n 48/ 78
6 (m + n) (m n) m n 6 6 = 2 3 2 3 49/ 78
6 (m + n) (m n) m n 6 6 = 2 3 2 3 50/ 78
6 m n (m + n) (m n) m n m n 2 3 51/ 78
6 m n (m + n) (m n) m n m n 2 3 52/ 78
6 3 m n 3 53/ 78
6 3 3 3 0 1 2 54/ 78
6 n 0 n 1 n 2 m 0 m 1 m 2 3 55/ 78
6 m n 3 0 (m + n) (m n) m n m n 3 56/ 78
6 n 0 n 1 n 2 m 0 m 1 m 2 57/ 78
6 n 0 n 1 n 2 m 0 m 1 m 2 58/ 78
6 1 2 59/ 78
6 m 1 n 1 m n m + n m n m n 0 (m + n) (m n) m n (m n) 3 60/ 78
6 m 1 n 1 m n m + n m n m n 0 (m + n) (m n) m n (m n) 3 61/ 78
6 n 0 n 1 n 2 m 0 m 1 m 2 62/ 78
6 n 0 n 1 n 2 m 0 m 1 m 2 63/ 78
6 m 2 n 1 m n m + n m n m + n 3 3 (m + n) (m n) m n (m + n) 3 64/ 78
6 m 2 n 1 m n m + n m n m + n 3 3 (m + n) (m n) m n (m + n) 3 65/ 78
6 n 0 n 1 n 2 m 0 m 1 m 2 66/ 78
6 n 0 n 1 n 2 m 0 m 1 m 2 67/ 78
6 m 2 n 2 m n m + n m n m n 0 (m + n) (m n) m n (m n) 3 68/ 78
6 m 2 n 2 m n m + n m n m n 0 (m + n) (m n) m n (m n) 3 69/ 78
6 n 0 n 1 n 2 m 0 m 1 m 2 70/ 78
6 n 0 n 1 n 2 m 0 m 1 m 2 71/ 78
6 m 1 n 2 m n m + n m n m + n 3 3 (m + n) (m n) m n (m + n) 3 72/ 78
6 m 1 n 2 m n m + n m n m + n 3 3 (m + n) (m n) m n (m + n) 3 73/ 78
6 n 0 n 1 n 2 m 0 m 1 m 2 74/ 78
6 n 0 n 1 n 2 m 0 m 1 m 2 3 75/ 78
6 76/ 78
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