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Re: Is x the square of an integer? [#permalink]
13 Nov 2013, 01:13
This post received KUDOS
Is x the square of an integer?
(1) x = 12k + 6, where k is a positive integer --> \(x=6(2k+1)=2*3(2k+1)\). Now, \(x\) to be a perfect square it should have an even power of its primes, but \(2k+1\) is an odd number and can no way produce 2 for \(x\). Thus \(x\) is not a perfect square. Sufficient.
(2) x = 3q + 9, where q is a positive integer --> \(x=3(q+3)\). If \(q=1\) then \(x=12\) and the answer is NO but if \(q=9\) then \(x=36\) and the answer is YES (basically if (q+3)=3*any perfect square then x will be a perfect square and if (q+3) is some other type of number then x won't be a perfect square). Not sufficient.