Divisibility of a prime

In summary, a prime number is a positive integer with only two factors, 1 and itself. To determine if a number is prime, it should not be divisible by any number other than 1 and itself. Knowing if a number is prime is important in many areas of mathematics, and not all prime numbers can be divided by 2. 1 is not considered a prime number because it only has one factor, itself.
  • #1
keityo
3
0
if p is any prime other than 2 or 5, prove that p divides infinitely many of the integers 9, 99, 999, 9999, ... If p is any prime other than 2 or 5, prove that p divides infinitely many of the integers 1, 11, 111, 1111, ...

Is there a way to do this problem using modular arithmetic? Thanks
 
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  • #2
Yes.
 
  • #3
I am stuck. Could you help me?
 
  • #4
Where are you stuck? What have you done so far?
 
  • #5
On getting started.
 
  • #6
keityo said:
On getting started.

Can you prove that at least 2 different powers of 10 have to be equal to each other mod p?
 
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1. What is the definition of a prime number?

A prime number is a positive integer that can only be divided evenly by 1 and itself. In other words, a prime number has exactly two factors.

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

To determine if a number is prime, you can check if it is divisible by any number other than 1 and itself. If it is not divisible by any other number, then it is a prime number.

3. Why is it important to know if a number is prime?

Knowing if a number is prime is important in many areas of mathematics, especially in number theory and cryptography. It also helps in simplifying fractions and finding common factors.

4. Can all prime numbers be divided by 2?

No, not all prime numbers can be divided by 2. The only prime number that is even is 2. All other prime numbers are odd.

5. Is 1 considered a prime number?

No, 1 is not considered a prime number. This is because it only has one factor, which is itself. Prime numbers must have exactly two factors.

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