't Hooft symbol
Imagine you have two numbers, let's call them 'a' and 'b'. Now, you want to know if a particular number 'x' is a quadratic residue of 'a' modulus 'b'. Hmm, that sounds pretty complicated, doesn't it?
Okay, let's break it down. What is a quadratic residue? It's basically a number that can be expressed as the square of another number. For example, 4 is a quadratic residue of 7 because 2^2 = 4 (2 is the number that when squared gives you 4).
What is modulus? It's like when you divide two numbers and the remainder is what is left over. So, remember when you learned division and your teacher told you that 6 divided by 4 is 1 with a remainder of 2? Modulus is just that '2' part. So, 6 mod 4 = 2.
The 't hooft symbol helps you figure out if a number is a quadratic residue of 'a' modulus 'b'. It's denoted by a strange looking '∝' symbol and it works like this:
If 'a' and 'b' are both odd numbers, then the 't hooft' symbol of 'a' and 'b' will be +1 if 'x' is a quadratic residue of 'a' modulus 'b', and -1 if 'x' is NOT a quadratic residue of 'a' modulus 'b'.
If either 'a' or 'b' is an even number, then the 't hooft' symbol of 'a' and 'b' will be +1 if 'x' is a quadratic residue of 'b' modulus 'a', and -1 if 'x' is NOT a quadratic residue of 'b' modulus 'a'.
So, basically, the 't hooft' symbol helps you figure out if a number can be expressed as the square of another number when you're dealing with remainders (modulus) of odd and even numbers. It's a fancy way of saying 'yes' or 'no'!
Okay, let's break it down. What is a quadratic residue? It's basically a number that can be expressed as the square of another number. For example, 4 is a quadratic residue of 7 because 2^2 = 4 (2 is the number that when squared gives you 4).
What is modulus? It's like when you divide two numbers and the remainder is what is left over. So, remember when you learned division and your teacher told you that 6 divided by 4 is 1 with a remainder of 2? Modulus is just that '2' part. So, 6 mod 4 = 2.
The 't hooft symbol helps you figure out if a number is a quadratic residue of 'a' modulus 'b'. It's denoted by a strange looking '∝' symbol and it works like this:
If 'a' and 'b' are both odd numbers, then the 't hooft' symbol of 'a' and 'b' will be +1 if 'x' is a quadratic residue of 'a' modulus 'b', and -1 if 'x' is NOT a quadratic residue of 'a' modulus 'b'.
If either 'a' or 'b' is an even number, then the 't hooft' symbol of 'a' and 'b' will be +1 if 'x' is a quadratic residue of 'b' modulus 'a', and -1 if 'x' is NOT a quadratic residue of 'b' modulus 'a'.
So, basically, the 't hooft' symbol helps you figure out if a number can be expressed as the square of another number when you're dealing with remainders (modulus) of odd and even numbers. It's a fancy way of saying 'yes' or 'no'!