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menager31
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Find all triples of primes (p,q,r), that pq+qr+rp and p^3+q^3+r^3−2pqr are divisible by p+q+r.
I really don't know how to start, (of course I've been trying)
I really don't know how to start, (of course I've been trying)
By "p2+ q2+ r2" do you mean p^2+ q^2+ r^2 ?AlephZero said:Hint: start by multiplying out (p+q+r)(p2 + q2 + r2)
AlephZero said:Hint: start by multiplying out (p+q+r)(p2 + q2 + r2)
A prime number is a positive integer that is only divisible by 1 and itself. In other words, it has exactly two factors.
Tasks involving prime numbers can be difficult because there are an infinite number of primes and they do not follow a predictable pattern, making it challenging to find and work with them.
Prime numbers are used in various real-life applications, such as cryptography, computer security, and coding theory. They are also used in creating secure passwords and in generating random numbers.
No, there is no known formula for generating prime numbers. The distribution of prime numbers is considered to be a random and unpredictable process.
Prime numbers are closely tied to many areas of mathematics, including number theory, algebra, and geometry. They have been the subject of study for centuries and continue to play a significant role in various mathematical concepts and theories.