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Expression and Square Sum (
Posted on 20160817
)
N is an odd positive integer .
Is the expression (3
^{3N}
 1)/( 3
^{N}
 1) always expressible as the sum of squares of two positive integers for every value of N?
Provide adequate reasoning for your answer.
No Solution Yet
Submitted by
K Sengupta
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solution
Comment 1 of 1
Express the numerator as the difference of cubes, givng the factors
(3^N  1) and (3^2N +3^N + 1).
The first factor cancels and the second is the sum of (3^N  1)^2 and 3^(N+1) which is square for odd N.
Posted by
xdog
on 20160817 10:47:06
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