Isserlis' theorem
Okay kiddo, have you heard of numbers that are perfect squares? These are the numbers that you get when you multiply a number by itself. For example, 1x1=1 and 2x2=4.
Now there is something called a quadratic residue, which is a fancy way of saying a number that is a perfect square. But not all numbers are quadratic residues. Some numbers cannot be written as the product of two equal numbers.
For Islerlis' theorem, we look at something called modular arithmetic. This is like doing arithmetic but only working with remainders. For example, if you divide 10 by 3, you get a remainder of 1.
Islerlis' theorem says that if you add up all the quadratic residues (remember, these are perfect squares) of a certain number when using modular arithmetic, the answer will always be the same, no matter what number you started with. This special answer is called a residue class.
It's kind of like a special code that all these numbers belong to and can be grouped together as. Isn't that cool, kiddo?
Now there is something called a quadratic residue, which is a fancy way of saying a number that is a perfect square. But not all numbers are quadratic residues. Some numbers cannot be written as the product of two equal numbers.
For Islerlis' theorem, we look at something called modular arithmetic. This is like doing arithmetic but only working with remainders. For example, if you divide 10 by 3, you get a remainder of 1.
Islerlis' theorem says that if you add up all the quadratic residues (remember, these are perfect squares) of a certain number when using modular arithmetic, the answer will always be the same, no matter what number you started with. This special answer is called a residue class.
It's kind of like a special code that all these numbers belong to and can be grouped together as. Isn't that cool, kiddo?
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