1/a^2 + 1/b^2 + … + 1/x^2 = 1/2

The equation

1/a^2   +   1/b^2   +   1/c^2   + … +   1/x^2   =   1/2

where all variables   a,   b,   c, …,   x   must be different, positive integers, and there must be a finite number of terms.
 
 

9   terms:

1/2   =  
1/2^2 + 1/3^2 + 1/4^2 + 1/5^2 + 1/7^2 + 1/8^2 + 1/56^2 + 1/168^2 + 1/840^2

 
 
10   terms:

1/2 =
1/2^2 + 1/3^2 + 1/4^2 + 1/5^2 + 1/6^2 + 1/12^2 + 1/30^2 + 1/60^2 + 1/75^2 + 1/100^2

 
 
11   terms:

1/2 =
1/2^2 + 1/3^2 + 1/4^2 + 1/5^2 + 1/6^2 + 1/12^2 + 1/30^2 + 1/50^2 + 1/100^2 + 1/150^2 + 1/300^2

 
 
Can you find more solutions?
 
 
 

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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.

One Response to 1/a^2 + 1/b^2 + … + 1/x^2 = 1/2

  1. Pingback: 1/a^2 + 1/b^2 + … + 1/x^2 = 1/2 | Benvitalis's Blog

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