What? No! if 6= (r)(s) then either r= 3 and s= 2 or r= 2 and s= 3 or r= 1 and s= 6 or r= 6 and r= 1. "If n= (r)(s), then r> 1 or s> 1" is true for all positive integers except 1.jonroberts74 said:An integer is prime if, and only if, n > 1 and for all positive integers r and s, if
n = (r)(s), then r > 1 or s > 1.
This is now true for all positive integers. What is true for prime numbers only is "If n= (r)(s) then r= 1 or s= 1."It should be if n = rs, then r great than or equal 1 or s greater than or equal 1
correct?
"N is prime if and only if" is a statement that means a number (N) is only considered prime if it meets the definition of a prime number. A prime number is a positive integer that is only divisible by 1 and itself.
To prove that a number is prime if and only if, you must show that it meets the definition of a prime number. This means that the number must be a positive integer and can only be divided by 1 and itself without any remainder. You can also use various mathematical methods such as the Sieve of Eratosthenes or the Fundamental Theorem of Arithmetic to prove a number is prime if and only if.
No, 1 is not considered a prime number under "N is prime if and only if." This is because 1 does not meet the definition of a prime number as it is only divisible by 1 and itself. Prime numbers must be divisible by exactly two distinct positive integers.
No, a number cannot be prime if and only if and also be composite. This is because a number is either prime or composite, but cannot be both at the same time. A prime number is only divisible by 1 and itself, while a composite number is divisible by more than two numbers.
The statement "N is prime if and only if" is used in various branches of mathematics, including number theory and algebra. It is often used to prove theorems and properties of prime numbers, as well as to determine the factors of a number. It is also used in cryptography and coding theory, where prime numbers play a crucial role.