Concatenation : A^2 || B^2 = C^2, (A=4,5,6,7,8.9)

 

A^2 \; || \; B^2 \; = \; C^2,   with   A \; = \; 4, \; 5, \; 6, \; 7, \; 8, \; 9
 

                                                               A \; = \; 4
 

4^2 \; || \; B^2 \; = \; C^2
 

41^2 \; = \; 1681 \; = \; 16 || 81 \; = \; 4^2 || 9^2

130^2 \; = \; 16900 \; = \; 16 || 900 \; = \; 4^2 || 30^2

410^2 \; = \; 168100 \; = \; 16 || 8100 \; = \; 4^2 || 90^2

1300^2 \; = \; 1690000 \; = \; 16 || 90000 \; = \; 4^2 || 300^2

4100^2 \; = \; 16810000 \; = \; 16 || 810000 \; = \; 4^2 || 900^2

13000^2 \; = \; 169000000 \; = \; 16 || 9000000 \; = \; 4^2 || 3000^2

41000^2 \; = \; 1681000000 \; = \; 16 || 81000000 \; = \; 4^2 || 9000^2

41225^2 \; = \; 1699500625 \; = \; 16 || 99500625 \; = \; 4^2 || 9975^2

129325^2 \; = \; 16724955625 \; = \; 16 || 724955625 \; = \; 4^2 || 26925^2

130000^2 \; = \; 16900000000 \; = \; 16 || 900000000 \; = \; 4^2 || 30000^2

410000^2 \; = \; 168100000000 \; = \; 16 || 8100000000 \; = \; 4^2 || 90000^2

412250^2 \; = \; 169950062500 \; = \; 16 || 9950062500 \; = \; 4^2 || 99750^2

 
 
                                                               A \; = \; 5
 

5^2 \; || \; B^2 \; = \; C^2
 

Jeff Curtis found:

160903431640625^2
= 25889914313729282379150390625
= 25 \; || \; 889914313729282379150390625
= 5^2 \; || \; 29831431640625^2

 
 
                                                               A \; = \; 6
 
6^2 \; || \; B^2 \; = \; C^2
 

190^2 \; = \; 36100 \; = \; 36 \; || \; 100 \; = \; 6^2 \; || \; 10^2

1900^2 \; = \; 3610000 \; = \; 36 \; || \; 10000 \; = \; 6^2 \; || \; 100^2

 
 
                                                               A \; = \; 7
 
7^2 \; || \; B^2 \; = \; C^2
 

223^2 \; = \; 49729 \; = \; 49 \; || \; 729 \; = \; 7^2 \; || \; 27^2

2225^2 \; = \; 4950625 \; = \; 49 \; || \; 50625 \; = \; 7^2 \; || \; 225^2

2230^2 \; = \; 4972900 \; = \; 49 \; || \; 72900 \; = \; 7^2 \; || \; 270^2

 
 
                                                               A \; = \; 8
 
8^2 \; || \; B^2 \; = \; C^2
 

Jeff Curtis found:

8009001265625^2 \; = \; 64144101272782851806640625

    64 \; || \; 144101272782851806640625 \; = \; 8^2 \; || \; 379606734375^2

 
 
 
                                                               A \; = \; 9
 

9^2 \; || \; B^2 \; = \; C^2
 

285^2 \; = \; 81225 \; = \; 81 \; || \; 225 \; = \; 9^2 \; || \; 15^2

905^2 \; = \; 819025 \; = \; 81 \; || \; 9025 \; = \; 9^2 \; || \; 95^2

2850^2 \; = \; 8122500 \; = \; 81 \; || \; 22500 \; = \; 9^2 \; || \; 150^2

 
 

Find more solutions

 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

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

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