# prime

1. ### Finding factors of a number

Hi, I hope someone can help. I am trying to developed an algorithm which based on a given input, call it x, determines whether x is prime. One way to do this is to check all the numbers (starting at 2) up to x/2 is divisible by x. If there is such a number, then x is not prime. I understand...
2. ### equivalent statements

Hi, I hope someone can help. Could someone please explain to me the reason behind why the following statement is false? The statement is as follows: “If n is a natural number then it may be expressed as a product of primes” is equivalent to “If n isn’t a natural number then it may not be...
3. ### Showing a Prime exists

Professor decided to give more "optional" homework. Let A = {4k +1 | k ∈ Z^+ }. Show that there exists a prime p of A, and elements j, k, of A, such that p | (jk), but p does not divide j or k. In words: "Let A equal the set of elements of 4k+1, where k is an element of all positive integers...
4. ### Prime Numbers

Hi, I am confused about this question: ​How many factors does x^2 y^3 z^3 have where xyz represents different prime numbers? Any help much appreciated, Thank you in advance, EbonyJade :)
5. ### If p>5 and 2p+1 are prime, prove that 3|4p+1

a.) Suppose that p>5 is prime and 2p+1 is also prime. Prove that 4p+1 is a multiple of 3. b.) Assume that p>5, 2p+1, (4p+1)/3, and 8p+1 are all prime. Prove that p is congruent to 29 (mod 30). I'm totally stumped. Any help would be greatly appreciated.
6. ### Proof: If q is a prime divisor of 2^p -1, then q ≡ 1 (mod p)

Let p be a prime number and M = 2^p − 1. Let q be a prime divisor of M. Prove that q ≡ 1 (mod p). I'm completely stuck. Help please?
7. ### Abstract algebra Polynomials and Prime

Let g(x) ∈ ℤ[x] have degree at least 2, and let p be a prime number such that: (i) the leading coefficient of g(x) is not divisible by p. (ii) every other coefficient of g(x) is divisible by p. (iii) the constant term of g(x) is not divisible by p^2. a) Show that if a ∈ ℤ such that [a]_p ≠...
8. ### Problem with prime number

x is a prime number. x is not 2 or 5. you need to prove that there are an infinity of powers of x which end in 001. --- I'm in dark, I really need a hint for this one. Thank you in advance.

10. ### Find y Prime

Find y prime. y = ln(x * root(x^2-1)) My work: y ' = 1/(x * root(x^2-1))*dy/dx (x * root(x^2-1)) I must apply the Product Rule. x*(1/2)(x^2-1)^(-1/2) + (x^2-1)^(1/2) y ' = 1/(x * root(x^2-1))*x*(1/2)(x^2-1)^(-1/2)(2x) + (x^2-1)^(1/2) y ' = 1/(x * root(x^2-1))*...
11. ### |g| a prime number

Show that if G is a finite group, then it contains at least one element g with |g| a prime number. (|g| is the order of g.) Hints only as this is an assignment problem.
12. ### Samsung Grand Prime 4G 1.2GHz processor With 1GB RAM!!

Samsung introduced Galaxy Grand Prime 4G smartphone pack with 5.00-inch 540x960 display powered by 1.2GHz processor alongside 1GB RAM and 8-megapixel rear camera. Doctor Who Season 9 Episode 3 Live StreamThe Leftovers Season 2 Episode 1 Live StreamThe Affair Season 2 Episode 1 Live StreamThe...
13. ### Need help in solving Radicals by using Prime Factorization

√112a3 It says I have to simplify it such as grouping similar numbers and forming it into a exponent. What I got so far is 24√7 = 2√7. Can anyone walk me through this process? Thanks.
14. ### Next set of prime birthdays for three brothers

Hello! I have the following problem: Three brothers are aged 6, 10 and 14 years old. Will they ever, in the future, have a prime number birthday the same year? Looking at all of the prime numbers between 1 and 100, it seems that they won't. So I guess this is the same thing as saying: are...
15. ### Odd Number and Prime

What is the basic difference between an odd number and prime number?
16. ### Solving for the prime factors?

421+221+1 I thought of setting x = 221, but I could not factor x2+x+1.
17. ### Is this the nature of prime numbers?

https://degroffsmodernprimenumbertheory.wordpress.com/ It appears to work for all of the prime numbers. The addendum is very important to tie it all together. What are some places I should submit this to?
18. ### Clarification regarding a proof

The following question is in the exercise of a book. I'd like to know if the proof that I've thought about fits the requirement. Question: Prove that there is no integral domain with exactly six elements. Can your argument be adapted to show that there is no integral domain with exactly four...
19. ### Prove that if p is a prime number larger than 3, then p^2 = 6k + 1 for some k ∈ ℤ.

PROBLEM STATEMENT:Prove that if p is a prime number larger than 3, then p^2 = 6k + 1 for some k ∈ ℤ.CORRECT SOLUTION:"Note that if p is a prime number larger than 3, then p mod 6 cannot be 0, 2, or 4 as this would mean p is even, and cannot be 3 as this would mean p is a multiple of 3.The only...
20. ### prime proof types, as in 3prime odd, 5 prime odd, and ...

is there 6-prime and 4-prime proofs? I suddenly cant find the references I thought I had. something like 1957 and 1971? I wanted to get the dates right