Concatenation : A^2 || B^2 = C^2, (A=1,2,3)

 

                                                             A \; = \; 1
 

1^2 \; || \; B^2 \; = \; C^2
 

35^2 \; = \; 1225 \; = \; 1 \; || \; 225 \; = \; 1^2 \; || \; 15^2

125^2 \; = \; 15625 \; = \; 1 \; || \; 5625 \; = \; 1^2 \; || \; 75^2

350^2 \; = \; 122500 \; = \; 1 \; || \; 22500 \; = \; 1^2 \; || \; 150^2

1250^2 \; = \; 1562500 \; = \; 1 \; || \; 562500 \; = \; 1^2 \; || \; 750^2

3500^2 \; = \; 12250000 \; = \; 1 \; || \; 2250000 \; = \; 1^2 \; || \; 1500^2

3925^2 \; = \; 15405625 \; = \; 1 \; || \; 5405625 \; = \; 1^2 \; || \; 2325^2

11125^2 \; = \; 123765625 \; = \; 1 \; || \; 23765625 \; = \; 1^2 \; || \; 4875^2

12500^2 \; = \; 156250000 \; = \; 1 \; || \; 56250000 \; = \; 1^2 \; || \; 7500^2

 
 

                                                             A \; = \; 2
 

2^2 \; || \; B^2 \; = \; C^2
 

65^2 \; = \; 4225 \; = \; 4 \; || \; 225 \; = \; 2^2 \; || \; 15^2

70^2 \; = \; 4900 \; = \; 4 \; || \; 900 \; = \; 2^2 \; || \; 30^2

205^2 \; = \; 42025 \; = \; 4 \; || \; 2025 \; = \; 2^2 \; || \; 45^2

650^2 \; = \; 422500 \; = \; 4 \; || \; 22500 \; = \; 2^2 \; || \; 150^2

700^2 \; = \; 490000 \; = \; 4 \; || \; 90000 \; = \; 2^2 \; || \; 300^2

2050^2 \; = \; 4202500 \; = \; 4 \; || \; 202500 \; = \; 2^2 \; || \; 450^2

2225^2 \; = \; 4950625 \; = \; 4 \; || \; 950625 \; = \; 2^2 \; || \; 975^2

6500^2 \; = \; 42250000  \; = \; 4 \; || \; 2250000 \; = \; 2^2 \; || \; 1500^2

7000^2 \; = \; 49000000  \; = \; 4 \; || \; 9000000 \; = \; 2^2 \; || \; 3000^2

 
 
                                                             A \; = \; 3
 

3^2 \; || \; B^2 \; = \; C^2
 

305^2 \; = \; 93025 \; = \; 9 \; || \; 3025 \; = \; 3^2 \; || \; 55^2

975^2 \; = \; 950625 \; = \; 9 \; || \; 50625 \; = \; 3^2 \; || \; 225^2

985^2 \; = \; 970225 \; = \; 9 \; || \; 70225 \; = \; 3^2 \; || \; 265^2

3050^2 \; = \; 9302500 \; = \; 9 \; || \; 302500 \; = \; 3^2 \; || \; 550^2

3075^2 \; = \; 9455625 \; = \; 9 \; || \; 455625 \; = \; 3^2 \; || \; 675^2

3125^2 \; = \; 9765625 \; = \; 9 \; || \; 765625 \; = \; 3^2 \; || \; 875^2

9625^2 \; = \; 92640625 \; = \; 9 \; || \; 2640625 \; = \; 3^2 \; || \; 1625^2

9750^2 \; = \; 95062500 \; = \; 9 \; || \; 5062500 \; = \; 3^2 \; || \; 2250^2

9850^2 \; = \; 97022500 \; = \; 9 \; || \; 7022500 \; = \; 3^2 \; || \; 2650^2

 

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About benvitalis

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

4 Responses to Concatenation : A^2 || B^2 = C^2, (A=1,2,3)

  1. Paul says:

    Here are a few

    35000^2 = 1225000000 = 1||225000000 = 1^2 || 15000^2
    39250^2 = 1540562500 = 1||540562500 = 1^2 || 23250^2
    110125^2 = 12127515625 = 1||2127515625 = 1^2 || 46125^2
    111250^2 = 12376562500 = 1||2376562500 = 1^2 || 48750^2
    125000^2 = 15625000000 = 1||5625000000 = 1^2 || 75000^2
    350000^2 = 122500000000 = 1||22500000000 = 1^2 || 150000^2
    392500^2 = 154056250000 = 1||54056250000 = 1^2 || 232500^2
    398125^2 = 158503515625 = 1||58503515625 = 1^2 || 241875^2
    1101250^2 = 1212751562500 = 1||212751562500 = 1^2 || 461250^2
    1112500^2 = 1237656250000 = 1||237656250000 = 1^2 || 487500^2
    1250000^2 = 1562500000000 = 1||562500000000 = 1^2 || 750000^2

    20500^2 = 420250000 = 4||20250000 = 2^2 || 4500^2
    22025^2 = 485100625 = 4||85100625 = 2^2 || 9225^2
    22250^2 = 495062500 = 4||95062500 = 2^2 || 9750^2
    65000^2 = 4225000000 = 4||225000000 = 2^2 || 15000^2
    70000^2 = 4900000000 = 4||900000000 = 2^2 || 30000^2
    205000^2 = 42025000000 = 4||2025000000 = 2^2 || 45000^2
    206125^2 = 42487515625 = 4||2487515625 = 2^2 || 49875^2
    220250^2 = 48510062500 = 4||8510062500 = 2^2 || 92250^2
    222500^2 = 49506250000 = 4||9506250000 = 2^2 || 97500^2
    646625^2 = 418123890625 = 4||18123890625 = 2^2 || 134625^2
    650000^2 = 422500000000 = 4||22500000000 = 2^2 || 150000^2
    700000^2 = 490000000000 = 4||90000000000 = 2^2 || 300000^2
    2050000^2 = 4202500000000 = 4||202500000000 = 2^2 || 450000^2
    2061250^2 = 4248751562500 = 4||248751562500 = 2^2 || 498750^2
    2202500^2 = 4851006250000 = 4||851006250000 = 2^2 || 922500^2
    2225000^2 = 4950625000000 = 4||950625000000 = 2^2 || 975000^2

    30500^2 = 930250000 = 9||30250000 = 3^2 || 5500^2
    30750^2 = 945562500 = 9||45562500 = 3^2 || 6750^2
    31250^2 = 976562500 = 9||76562500 = 3^2 || 8750^2
    96250^2 = 9264062500 = 9||264062500 = 3^2 || 16250^2
    97500^2 = 9506250000 = 9||506250000 = 3^2 || 22500^2
    98500^2 = 9702250000 = 9||702250000 = 3^2 || 26500^2
    305000^2 = 93025000000 = 9||3025000000 = 3^2 || 55000^2
    307500^2 = 94556250000 = 9||4556250000 = 3^2 || 67500^2
    312500^2 = 97656250000 = 9||7656250000 = 3^2 || 87500^2
    962500^2 = 926406250000 = 9||26406250000 = 3^2 || 162500^2
    966625^2 = 934363890625 = 9||34363890625 = 3^2 || 185375^2
    975000^2 = 950625000000 = 9||50625000000 = 3^2 || 225000^2
    985000^2 = 970225000000 = 9||70225000000 = 3^2 || 265000^2
    3050000^2 = 9302500000000 = 9||302500000000 = 3^2 || 550000^2
    3075000^2 = 9455625000000 = 9||455625000000 = 3^2 || 675000^2
    3091875^2 = 9559691015625 = 9||559691015625 = 3^2 || 748125^2
    3105125^2 = 9641801265625 = 9||641801265625 = 3^2 || 801125^2
    3125000^2 = 9765625000000 = 9||765625000000 = 3^2 || 875000^2

    Paul

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