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No.

First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.

Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theorem

No.

First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.

Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theorem

No.

First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.

Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theorem

No.

First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.

Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theorem

Q: Can you write every integer as the sum of two nonzero perfect squares?

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Every integer is a rational number, and some integers are perfect squares. These are the only rational numbers to have an integral square root.

Every integer is a rational number.

Every integer is rational.

Yes, 1 is a factor of every integer and every integer is a multiple of 1.

No. Consider four points at the corners of a perfect square.

Related questions

The square root of every perfect square is an integer. However, there are also square roots of numbers that are not perfect squares.

Positive

Every integer is a rational number, and some integers are perfect squares. These are the only rational numbers to have an integral square root.

I'm not sure you've given us enough information. Every nonzero integer can be a factor, so unless you have a specific number in mind, your answer is potentially any nonzero number except 11.

Every value of 24 multiplied by a non-zero positive integer. i.e. 24, 48, 72, 96... etc

Perfect squares.

Every nonzero number has multiples. Every set of nonzero numbers has an LCM.

The only common factor of every nonzero integer is 1.

Yes, since one is a perfect square. But that's not helpful. Other than one, not every integer has a factor with an integral square root.

In the complex field, every number is a square so there are no numbers that are not squares. If the domain is reduced to that of real numbers, any negative number is not a square. However, the term "square numbers" (not number's!) is often used to refer to perfect square numbers. These are numbers that are squares of integers. Therefore the squares of fractions or Irrational Numbers are non-squares.

Yes

Yes! it is.