Let (a, b, c) denote a triplet of distinct integers in an ascending order.
If
a2+ b2=c2+1 or if
a2+ b2=c2- 1 we will call such a triplet an
ARAT (since it represents an almost-right-angle triangle) .
(4,8,9) is such a triplet.
How many ARATs are there, provided c<1,000,000?
(In reply to
programming mistake; also need faster computer/programming language by Charlie)
The new version starts off by reporting the first 100 counted:
4 7 8
4 8 9 *
8 9 12
7 11 13
6 17 18
6 18 19 *
11 13 17
10 15 18
9 19 21
14 17 22
13 19 23
17 21 27
8 31 32
16 23 28
8 32 33 *
11 29 31
15 26 30
14 31 34
20 25 32
19 27 33
18 30 35 *
17 34 38
23 29 37
22 31 38
13 41 43
16 41 44
10 49 50
26 33 42
10 50 51 *
25 35 43
19 43 47
23 41 47
31 34 46
29 37 47
28 39 48
22 46 51 *
15 55 57
34 38 51 *
32 41 52
21 53 57
25 49 55
31 43 53
24 55 60
35 45 57
34 47 58
12 71 72
12 72 73 *
20 65 68
23 64 68
31 56 64
38 49 62
17 71 73
37 51 63
26 65 70
41 53 67
40 55 68
29 67 73
33 64 72
49 50 70
22 79 82
25 76 80
44 57 72
43 59 73
28 76 81 *
41 64 76
51 55 75
19 89 91
31 77 83
47 61 77
46 63 78
39 71 81
14 97 98
14 98 99 *
44 68 81 *
34 79 86
43 71 83
50 65 82
27 89 93
49 67 83
41 79 89
53 69 87
52 71 88
36 89 96
56 73 92
21 109 111
39 91 99
55 75 93
29 103 107
32 100 105 *
47 86 98
35 99 105
59 77 97
26 111 114
58 79 98
69 71 99
65 76 100
41 101 109
16 127 128
49 94 106
62 81 102
we'll see in a couple of hours, what the total number is.
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Posted by Charlie
on 2016-09-07 10:41:16 |
re: programming mistake; also need faster computer/programming language
