SOLUTION: Prove that the number {{{ (2n+1)^3-(2n-1)^3 }}} can be written as the sum of three squares.
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Question 1019845: Prove that the number can be written as the sum of three squares.
Found 2 solutions by LinnW, ikleyn:
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
expands to
expands to
So =
-
=
Check the answer using www.wolframalpha.com
Answer by ikleyn(52835) (Show Source): You can put this solution on YOUR website!
.
Prove that the number can be written as the sum of three squares.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let me continue from the other post.
To complete the proof, we only need to represent 24n^2 + 2 as the sum of three square.
It is easy:
= + + = + + .
The statement is proved.
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