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Generation of Pythagorean Triples from Reciprocals

First 22 Whole Numbers

(p = x, q = 2)

Note: The first three lines are not mathematically sound

p p/q

q/p

(p2 - q2) /2pq

(p2 + q2) /2pq

[(p2 + q2) /2pq]2

(p/q-q/p)/2

(p/q+q/p)/2

Prod

a

c

b

4

2.00

0.50000000

12.00000000

20.00000000

400.00000000

0.7500000000

1.2500000000

4

3

5

4

5

2.50

0.40000000

16.80000000

23.20000000

538.24000000

1.0500000000

1.4500000000

1

21

29

20

6 3.00 0.33333333 21.33333333 26.66666667 711.11111111 1.3333333333 1.6666666667 8 4 5 3
7 3.50 0.28571429 25.71428571 30.28571429 917.22448980 1.6071428571 1.8928571429 1 45 53 28
8 4.00 0.25000000 30.00000000 34.00000000 1156.00000000 1.8750000000 2.1250000000 4 15 17 8
9 4.50 0.22222222 34.22222222 37.77777778 1427.16049383 2.1388888889 2.3611111111 1 77 85 36
10 5 0.20000000 38.40000000 41.60000000 1730.56000000 2.4000000000 2.6000000000 8 12 13 5
11 5.50 0.18181818 42.54545455 45.45454545 2066.11570248 2.6590909091 2.8409090909 1 117 125 44
12 6.00 0.16666667 46.66666667 49.33333333 2433.77777778 2.9166666667 3.0833333333 4 35 37 12
13 6.50 0.15384615 50.76923077 53.23076923 2833.51479290 3.1730769231 3.3269230769 1 165 173 52
14 7.00 0.14285714 54.85714286 57.14285714 3265.30612245 3.4285714286 3.5714285714 8 24 25 7
15 7.50 0.13333333 58.93333333 61.06666667 3729.13777778 3.6833333333 3.8166666667 1 221 229 60
16 8.00 0.12500000 63.00000000 65.00000000 4225.00000000 3.9375000000 4.0625000000 4 63 65 16
17 8.50 0.11764706 67.05882353 68.94117647 4752.88581315 4.1911764706 4.3088235294 1 285 293 68
18 9 0.11111111 71.11111111 72.88888889 5312.79012346 4.4444444444 4.5555555556 8 40 41 9
19 9.50 0.10526316 75.15789474 76.84210526 5904.70914127 4.6973684211 4.8026315789 1 357 365 76
20 10.00 0.10000000 79.20000000 80.80000000 6528.64000000 4.9500000000 5.0500000000 4 99 101 20
21 10.50 0.09523810 83.23809524 84.76190476 7184.58049887 5.2023809524 5.2976190476 1 437 445 84
22 11.00 0.09090909 87.27272727 88.72727273 7872.52892562 5.4545454545 5.5454545455 8 60 61 11

 

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