A^2 + B^2 = C^{4k+2} + 1

 
 

n^6 + 1 = (n^3 - 2n)^2 + (2n^2 - 1)^2

n^{10} + 1 = (n^5 - 2n^3 + 2n)^2 + (2n^4 - 2n^2 + 1)^2

n^{14} + 1 = (n^7 - 2n^5 + 2n^3 - 2n)^2 + (2n^6 - 2n^4 + 2n^2 - 1)^2

n^{18} + 1 = (n^9 - 2n^7 + 2n^5 - 2n^3 + 2n)^2 + (2n^8 - 2n^6 + 2n^4 - 2n^2 + 1)^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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