Is 1 a square number?

No, 1 is not a square number because it does not have two equal factors. The only factor of 1 is 1 itself.

How can we check if a given number is a perfect square or not?

We can check if a given number is a perfect square or not by taking its square root and checking if it is an integer. If it is an integer, then the given number is a perfect square; otherwise, it’s not. For example, the square root of 36 is 6 (an integer), so 36 is a perfect square. On the other hand, the square root of 35.5 is not an integer, so 35.5 is not a perfect square.

Can every positive integer be expressed as a sum of two squares?

No, not every positive integer can be expressed as a sum of two squares. A positive integer can be written as a sum of two squares if and only if its prime factorization does not contain any prime congruent to 3 mod 4 raised to an odd power. For example, the number 7 cannot be expressed as a sum of two squares because it is an odd prime and it is congruent to 3 modulo 4.

Are there any patterns in the sequence of square numbers?

Yes, there is a pattern in the sequence of square numbers. The sequence of square numbers can be expressed as an arithmetic progression with a common difference of 2n+1, where n is the position of the number in the sequence starting from zero.

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