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How many factors does 2p have if p is an odd prime number?
It has four factors: 1, 2, p, and 2p.
Why is the product of two odd numbers is odd?
Here's the following proof that "product of two odd numbers is odd". Proof: Any odd number can be written in the form 2p+1. Let your first odd number be written in this form. Let your second odd number be written as 2q+1 - essentially the same form as above, but since p may not equal q, separate variables are used. Thus: First odd number x second odd number = (2p+1)(2q+1) = 2pq + 2p +2q +1. The plus one on the end indicates that the product is odd, as required.
Is odd times odd always odd?
Yes, it's always odd, and here's the proof: All odd numbers can be expressed as 2p + 1, where p is any integer. Multiply two of those together: (2n + 1)(2p + 1) = 4np + 2n + 2p + 1 = 2(np + n + p) + 1. Since both np, n, and p are integers, that means np + n + p is an integer; and since that integer is being multiplied by 2, it must be even. Thus, by adding 1 to that even number, the result will be odd.
What is a mersume prime number?
Let p = any prime number. (2p -1) is called a Mersenne number. Any such number that is prime is called a Mersenne Prime. Father Mersenne wrote a list of numbers of this type which he thought were prime, but a few were not. In fact, most of the large Mersenne numbers are not prime, but all the really large numbers that have been proved to be prime are Mersenne Primes.
What is a prime number that is one more than a square number?
A prime number that is one more than a square number is known as a Sophie Germain prime. Sophie Germain primes are of the form 2p+1, where p is a prime number. For example, 17 is a Sophie Germain prime because it is one more than the square of 4, and both 4 and 17 are prime numbers. Sophie Germain primes have applications in number theory and cryptography.
