Equation: x^2 + (x+1)(x+2) = y^2

 
 
x^2 \; + \; (x+1) \,(x+2) \; = \; y^2

x, y   are positive integers.

 
Here are the first few solutions:

 
2^2 \; + \; (3\times 4) \; = \; 4^2

7^2 \; + \; (8\times 9) \; = \; 11^2

94^2 \; + \; (95\times 96) \; = \; 134^2

263^2 \; + \; (264\times 265) \; = \; 373^2

3218^2 \; + \; (3219\times 3218) \; = \; 4552^2

8959^2 \; + \; (8960\times 8961) \; = \; 12671^2

109342^2 \; + \; (109343\times 109344) \; = \; 154634^2

304367^2 \; + \; (304368\times 304369) \; = \; 430441^2

3714434^2 \; + \; (3714435\times 3714436) \; = \; 5253004^2

10339543^2 \; + \; (10339544\times 10339545) \; = \; 14622323^2

126181438^2 \; + \; (126181439\times 126181440) \; = \; 178447502^2

351240119^2 \; + \; (351240120\times 351240121) \; = \; 496728541^2

4286454482^2 \; + \; (4286454483\times 4286454484)
= \; 6061962064^2

11931824527^2 \; + \; (11931824528\times 11931824529)
= \; 16874148071^2

145613270974^2 \; + \; (145613270975\times 145613270976)
= \; 205928262674^2

405330793823^2 \; + \; (405330793824\times 405330793825)
= \; 573224305873^2

4946564758658^2 \; + \; (4946564758659\times 4946564758660)
= \; 6995498968852^2

13769315165479^2 \; + \; (13769315165480\times 13769315165481)
= \; 19472752251611^2

168037588523422^2 \; + \; (168037588523423\times 168037588523424)
= \; 237641036678294^2

467751384832487^2 \; + \; (467751384832488\times 467751384832489)
= \; 661500352248901^2

5708331445037714^2 \; + \; (5708331445037715\times 5708331445037716)
= \; 8072799748093144^2

 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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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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