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The proposition in the question is simply not true so there can be no answer!
For example, if given the integer 6:
there are no two perfect squares whose sum is 6,
there are no two perfect squares whose difference is 6,
there are no two perfect squares whose product is 6,
there are no two perfect squares whose quotient is 6.
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Can 8081 be the sum of two perfect squares?
8081 can be the sum of two perfect squares because its perfect squares are 41 x41+80x80=1681+6400. Answer=1681+6400
Counter example that a positive integer is not equal to the sum of two squares?
3 is the smallest integer that cannot be written as the sum of two squares. This is easy to see, since the only squares less than or equal to 3 are 0 and 1.
What you have learn in product of perfect square?
That the set of perfect squares is closed under multiplication. That is if x and y are any two perfect squares, then x*y is a perfect square.
What two square numbers total 21?
There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.
Can you write every integer as the sum of two nonzero perfect squares?
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_theoremNo.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_theoremNo.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_theoremNo.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
