Prime number and the coefficients of polynomial

In summary, a prime number is a positive integer with only two factors - 1 and itself. To determine if a number is prime, you can check if it is divisible by any numbers between 2 and the square root of the number. Prime numbers are important in cryptography and have various applications in fields such as computer science and physics. The coefficients of a polynomial are the numerical values multiplied by the variables in each term, and prime numbers are often used in the process of factoring polynomials.
  • #1
anemone
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MHB
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Hi,
I've got an equation stating p=a(r-1).
If p represents prime number and r is a positive integer, and a is a constant, what can we conclude for the constant a?
Like a $\in${-1, 1, -p, p}?
I suspect this has something to do with modular arithmetic...:confused:

Thanks.
 
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  • #2
About all we can say is that either
(1) a = 1 and r = p+1
or
(2) a = p and r = 2.
 
  • #3
It has everything to do with the definition of "prime number"- a number whose only factors are 1 and itself. Thus giving awkwards response.
 

FAQ: Prime number and the coefficients of polynomial

What is a prime number?

A prime number is a positive integer that is only divisible by 1 and itself. In other words, it has exactly two factors.

How do I determine if a number is prime?

To determine if a number is prime, you can check if it is divisible by any numbers between 2 and the square root of the number. If it is not divisible by any of these numbers, then it is a prime number.

What is the importance of prime numbers?

Prime numbers play a crucial role in cryptography, which is used to secure sensitive information. They are also important in number theory and have various applications in computer science, physics, and other fields.

What are the coefficients of a polynomial?

The coefficients of a polynomial are the numerical values that are multiplied by the variables in each term. For example, in the polynomial 3x^2 + 5x + 2, the coefficients are 3, 5, and 2.

How are prime numbers related to the coefficients of a polynomial?

Prime numbers are often used in the process of factoring polynomials. The prime factors of the coefficients can help determine the possible factors of the polynomial, making it easier to factor and solve equations.

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