Three numbers are coprime if they do not have any common factors other than 1. In other words, their greatest common divisor is 1. For example, 4, 9, and 13 are coprime because the only positive integer that divides all three of them is 1.
To prove that three numbers are coprime, you can use the Euclidean algorithm to find their greatest common divisor. If the greatest common divisor is 1, then the numbers are coprime. Alternatively, you can also check if the prime factorization of each number has no common factors.
No, if two numbers are not coprime, then their greatest common divisor is greater than 1. This means that any combination of these two numbers and a third number will also have a greatest common divisor greater than 1, and therefore, the three numbers cannot be coprime.
The expression (an + bn + cn) / abc is used to test if three numbers (a, b, and c) are coprime. If the expression simplifies to an integer, then the numbers are coprime. If the expression does not simplify to an integer, then the numbers are not coprime.
Yes, the expression (an + bn + cn) / abc can be used as a proof or disproof of coprime numbers. If the expression simplifies to an integer, then it proves that the three numbers are coprime. If the expression does not simplify to an integer, then it disproves the claim that the numbers are coprime.