perplexus.info :: Just Math : Expression and Square Sum

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.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The expression 3^3n -1/(3^n-1) is always expressible as the sum of squares for every odd value of n.
The property may NOT hold for every even value of n.
For example, when n=2, the value of the expression is 91 which is NOT expressible as the sum of two squares.
For an explanation, refer to the solution submitted by xdog in this location.

Comments: ( You must be logged in to post comments.)

	Subject	Author	Date
	solution	xdog	2016-08-17 10:47:06

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