Based on my research, I found that there are many arguments about this statement, the main factor is the true definition of perfect square. Some said they are the squares of the whole numbers, but some said that any number that can be written as a positive integer to the power of two and some said that an integer that can be expressed as the product of two equal integers.
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9Of course it is. – Brian M. Scott Nov 27 '20 at 04:30
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8"any number that can be written as a POSITIVE integer to the power of two" Curious. It seems obvious that the adjective POSITIVE should be replaced with NON-NEGATIVE. Can you cite the source for this particular quote? – user2661923 Nov 27 '20 at 04:33
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6Whether or not $0$ is included in the definition of a square is a matter of convention - just as whether or not $,0\in\Bbb N,,$ or whether or not $0$ is positive. For example, in modular arithmetic many authors exclude $0$ from modular squares (quadratic residues) for convenience. – Bill Dubuque Nov 27 '20 at 08:46
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1An interesting point to ponder: The perfect square of any non-zero integer has a finite (and odd) number of positive integer divisors. $0=0^2$ has an infinite number of such divisors. If $0$ is to be considered a perfect square, it is unique in this respect. – Keith Backman Nov 27 '20 at 17:36
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A perfect square is the square of an integer – or nonnegative integer, without loss of generality, since $(-x)^2=x^2$. Since $0=0^2$, $0$ is a perfect square.
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