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is it true that
(a+b)^p = a^p + b^p (mod p)
(a,b,p natural)
only if (p-1)! and p are coprime?
(a+b)^p = a^p + b^p (mod p)
(a,b,p natural)
only if (p-1)! and p are coprime?
p-1! and p a coprime if and only if p is prime
Why is it ambiguous? (p-1)! and p are coprime iff p is prime, so the statement can be reworded:matt grime said:wel,, p-1! and p a coprime if and only if p is prime, but unless you introduce some quantifiers it is anbiguous.
Coprime numbers are two or more numbers that do not have any common factors other than 1. In other words, their greatest common divisor (GCD) is 1.
Coprime numbers play a crucial role in many mathematical concepts such as prime factorization, modular arithmetic, and cryptography. They also have applications in fields like number theory, coding theory, and computer science.
To determine if two numbers are coprime, you can calculate their GCD using Euclid's algorithm. If the GCD is 1, then the numbers are coprime. Alternatively, you can also check if the numbers have any common prime factors, if not, then they are coprime.
Some examples of coprime numbers are 3 and 5, 8 and 9, 13 and 17, and 21 and 25. These numbers do not have any common factors other than 1.
Yes, all prime numbers are coprime since they only have 1 and themselves as factors. Therefore, they do not have any common factors with any other number.