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Number Theory Math History question - Fibonacci Proof

wreader

New member
Feb 7, 2014
1
Can someone please help me with the following:

Prove that if the sum of two consecutive intergers is a square than the square of the larger integer will equal the sum of the nonzero squares.

Hint: if n+(n-1) = h^2 then h is odd.

Not really sure where to start.

Thanks in advance
 
Last edited:

mathbalarka

Well-known member
MHB Math Helper
Mar 22, 2013
573
Well, $n + (n + 1) = 2n + 1$ is a square by what is given and $(n + 1)^2$ is ... ?