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Expression and Square Sum (Posted on 2016-08-17)

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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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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 2016-08-17 10:47:06

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