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Counting ARATs (Posted on 2016-09-07) Difficulty: 3 of 5
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?

No Solution Yet Submitted by Ady TZIDON    
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re: programming mistake; also need faster computer/programming language | Comment 2 of 4 |
(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.

  Posted by Charlie on 2016-09-07 10:41:16
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