Sums and products of pairs of num3ers are squares

 

                                                       a   +   b   =   x^2
                                                       a   *   b    =   y^2

 
 
Here are the first few examples
 
2^2 = 2 + 2
2^2 = 2 * 2

4^2 = 8 + 8 = 16              2^3 + 2^3 = 4^2
8^2 = 8 * 8

5^2 = 16 + 9 = 25              4^2 + 3^2 = 5^2
12^2 = 16 * 9 = 144

6^2 = 18 + 18 = 36
18^2 = 18 * 18

8^2 = 32 + 32 = 64              2^5 + 2^5 = 2^6
32^2 = 32 * 32

10^2 = 2 + 98 = 100
14^2 = 2 * 98 = 196

10^2 = 10 + 90 = 100 = 10^2
30^2 = 10 * 90 = 900

10^2 = 36 + 64 = 100              6^2 + 8^2 = 10^2
48^2 = 36 * 64 = 2304

10^2 = 50 + 50 = 100
50^2 = 50 * 50 = 2500

12^2 = 72 + 72 = 144
72^2 = 72 * 72

13^2 = 25 + 144 = 169              5^2 + 12^2 = 13^2
60^2 = 25 * 144 = 3600

13^2 = 52 + 117 = 169
78^2 = 52 * 117 = 6084

14^2 = 98 + 98 = 196
98^2 = 98 * 98

15^2 = 45 + 180
90^2 = 45 * 180 = 8100

15^2 = 81 + 144 = 225              9^2 + 12^2 = 15^2
108^2 = 81 * 144 = 11664

16^2 = 128 + 128 = 256
128^2 = 128 * 128

17^2 = 17 + 272 = 289
68^2 = 17 * 272 = 4624

17^2 = 64 + 225 = 289              8^2 + 15^2 = 17^2
120^2 = 64 * 225 = 14400

18^2 = 162 + 162 = 324
162^2 = 162 * 162

20^2 = 8 + 392 = 400
56^2 = 8 * 392 = 3136

20^2 = 40 + 360 = 400
120^2 = 40 * 360 = 14400

20^2 = 80 + 320 = 400
160^2 = 80 * 320 = 25600

20^2 = 144 + 256 = 400              12^2 + 16^2 = 20^2
192^2 = 144 * 256 = 36864

20^2 = 200 + 200 = 400
200^2 = 200 * 200 = 40000

 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Math Beauty, Number Puzzles and tagged , , . Bookmark the permalink.

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