Prime numbers and divisibility

In summary, prime numbers are positive integers that are only divisible by 1 and themselves. To determine if a number is prime, you can divide it by all the numbers between 2 and the square root of the number. Prime numbers are different from composite numbers, which have more than two factors. All numbers can be expressed as a product of prime numbers, according to the fundamental theorem of arithmetic. Prime numbers are important in cryptography because they are used in generating secure encryption keys and algorithms for data encryption and decryption.
  • #1
terafull
3
0
Find all prime numbers [tex](p,q,r)[/tex], that numbers [tex]pq+pr+rq[/tex] and [tex]p^3+q^3+r^3-2pqr[/tex] are divided by [tex]p+q+r[/tex]
 
Physics news on Phys.org
  • #2
I'm seeing this problem asked a lot on the various math forums I frequent. Where does it come from?
 
  • #3
Which forums (fora) are those, CR?

(See it this way: if you tell me I'll go pester somewhere else.) :P
 
  • #4
Doesn't looking at the problem just make you instantly think of cubing things?
 
  • #5
I think I saw the problem, at the least, at
http://www.mymathforum.com/
 

1. What are prime numbers?

Prime numbers are positive integers that are only divisible by 1 and themselves. Examples of prime numbers include 2, 3, 5, 7, 11, and so on.

2. How do I determine if a number is prime?

To determine if a number is prime, you can divide it by all the numbers between 2 and the square root of the number. If the number is only divisible by 1 and itself, then it is a prime number.

3. What is the difference between prime and composite numbers?

Prime numbers are numbers that are only divisible by 1 and themselves, while composite numbers have more than two factors. For example, 6 is a composite number because it is divisible by 1, 2, 3, and 6.

4. Can all numbers be expressed as a product of prime numbers?

Yes, this is known as the fundamental theorem of arithmetic. It states that every positive integer can be expressed as a unique product of prime numbers.

5. Why are prime numbers important in cryptography?

Prime numbers play a crucial role in cryptography as they are used in generating large, secure encryption keys. They are also used in algorithms for data encryption and decryption.

Similar threads

MHB Show that the groups are abelian
    • Linear and Abstract Algebra
Replies
1
Views
784
MHB Prove R is a Sub-ring of $\mathbb{Q}$ - Prime $p \in \mathbb{Z}$
    • Linear and Abstract Algebra
Replies
11
Views
1K
I Understanding the Results of gcd(x,n)
    • Linear and Abstract Algebra
Replies
8
Views
897
I Confused about Gauss's Lemma of Irreducibility
    • Linear and Abstract Algebra
Replies
4
Views
1K
I Irreducible polynomials and prime elements
    • Linear and Abstract Algebra
Replies
5
Views
922
I Question on Primitive Roots and GCDs
    • Linear and Abstract Algebra
Replies
2
Views
789
I P-adic valuation expression for a given natural number
    • Linear and Abstract Algebra
Replies
9
Views
2K
I Frequency of prime number gaps according to (p-1)/(p-2)
    • Linear and Abstract Algebra
Replies
2
Views
801
I Why do the lines m and l coincide in the proof of the parallelogram rule?
    • Linear and Abstract Algebra
Replies
4
Views
694
I ##(p^k -1) \equiv X \mbox{(mod p)}## via Wilson's theorem
    • Linear and Abstract Algebra
Replies
2
Views
857

Hot Threads

Recent Insights

Back
Top