If we are given that a perfect square say x^2 is divisible by n (a non perfect square integer) then it is always true that x^2 = k* n^2?
Is it always true?
Just wanted comments on this?
No, that is not always true, at least if you mean for k to be an integer. If you take x^2 = 16, say, then x^2 is divisible by 8, but not by 8^2.
It *is* however true when n is prime. That is, if x is an integer, and x^2 is divisible by a prime p, then x^2 is certainly divisible by p^2.
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