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What are the factors and composite factors of 15?
A number will have 12 factors if it satisfies any of the following prime factor configurations: P11 (P1)5*(P2) (P1)3*(P2)2 (P1)2*(P2)*(P3)
What are the factors of p2-2p plus 2?
p2 - 2p + 2 can be factored as (p - 1)(p - 1)which can be written as ( p - 1)2.
Is Composite numbers have only 2 factors?
It depends on whether 1 is considered a factor. If yes, then the answer to the question is no, since 1 and the number itself are the two factors implying that it is a prime. If 1 is not considered as a factor, then the square of any prime meets the requirements. If p is a prime, then p and p2 are the only two factors of p2.
What is the pmf of trinomial distribution?
P(x=n1,y=n2) = (n!/n1!*n2!*(n-n1-n2)) * p1^n1*p2^n2*(1-p1-p2) where n1,n2=0,1,2,....n n1+n2<=n
What is the mathematical proof to show that the number of prime numbers is infinite?
The proof is by contradiction: assume there is a finite number of prime numbers and get a contradiction by requiring a prime that is not one of the finite number of primes. Suppose there are only a finite number of prime numbers. Then there are n of them.; and they can all be listed as: p1, p2, ..., pn in order with there being no possible primes between p(r) and p(r+1) for all 0 < r < n. Consider the number m = p1 × p2 × ... × pn + 1 It is not divisible by any prime p1, p2, ..., pn as there is a remainder of 1. Thus either m is a prime number itself or there is some other prime p (greater than pn) which divides into m. Thus there is a prime which is not in the list p1, p2, ..., pn. But the list p1, p2, ..., pn is supposed to contain all the prime numbers. Thus the assumption that there is a finite number of primes is false; ie there are an infinite number of primes. QED.
