[Hardest Maths Statement Puzzle] Toughest Math Statement Question

Toughest Math Statement Question
(Source : http://hardest-puzzle.blogspot.com/2...-question.html
)

I am thinking of a 6-digit number. The sum of the digits is 43.

And only two of the following three statements about the number are
true:

(1) it's a square number,
(2) it's a cube number, and
(3) the number is under 500000.

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http://hardest-puzzle.blogspot.com/2...-question.html

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