Robinson congruences
OK little one, let me explain what Robinson congruences are.
Have you ever played with Lego blocks? You know how they come in different sizes and colors, right? Well, think of numbers as Lego blocks too. Just like the different sizes of Lego blocks, numbers can also have different properties. One of these properties is called congruence.
When we talk about two numbers being congruent, it means that they have the same remainder when divided by a certain number. For example, let's say we have the numbers 11 and 5. If we divide 11 by 3, we get a remainder of 2. If we divide 5 by 3, we get a remainder of 2 as well. This means that 11 and 5 are congruent modulo 3 (which is a fancy way of saying "when we divide by 3"). Usually we write this as 11 ≡ 5 (mod 3).
Now, Robinson congruences are a special type of congruence that have to do with something called the "order" of a number. The order of a number is the smallest number you can raise it to and get a result of 1.
For example, the order of 2 modulo 7 is 3, because 2^3 = 8 ≡ 1 (mod 7).
Now, let's say we have two numbers, a and b, that are coprime (which means that the only positive integer that divides both of them is 1). If we know the order of a modulo b and the order of b modulo a, we can use this information to find all the Robinson congruences between a and b.
Robinson congruences are written as a ≡ b (mod p^k), where p is a prime number and k is a positive integer. These congruences tell us that a and b have the same remainders when divided by powers of certain primes.
So, in short, Robinson congruences are a special type of congruence that tell us about the remainders of two numbers that are coprime, based on their orders modulo each other. They are written in a specific way that involves prime numbers and exponents.
Have you ever played with Lego blocks? You know how they come in different sizes and colors, right? Well, think of numbers as Lego blocks too. Just like the different sizes of Lego blocks, numbers can also have different properties. One of these properties is called congruence.
When we talk about two numbers being congruent, it means that they have the same remainder when divided by a certain number. For example, let's say we have the numbers 11 and 5. If we divide 11 by 3, we get a remainder of 2. If we divide 5 by 3, we get a remainder of 2 as well. This means that 11 and 5 are congruent modulo 3 (which is a fancy way of saying "when we divide by 3"). Usually we write this as 11 ≡ 5 (mod 3).
Now, Robinson congruences are a special type of congruence that have to do with something called the "order" of a number. The order of a number is the smallest number you can raise it to and get a result of 1.
For example, the order of 2 modulo 7 is 3, because 2^3 = 8 ≡ 1 (mod 7).
Now, let's say we have two numbers, a and b, that are coprime (which means that the only positive integer that divides both of them is 1). If we know the order of a modulo b and the order of b modulo a, we can use this information to find all the Robinson congruences between a and b.
Robinson congruences are written as a ≡ b (mod p^k), where p is a prime number and k is a positive integer. These congruences tell us that a and b have the same remainders when divided by powers of certain primes.
So, in short, Robinson congruences are a special type of congruence that tell us about the remainders of two numbers that are coprime, based on their orders modulo each other. They are written in a specific way that involves prime numbers and exponents.