Proving the Divisibility of 8 and Odd Squares

In summary, Prime Division is a mathematical concept involving dividing a number into its prime factors. This is done through a process called prime factorization, which helps us understand the fundamental building blocks of numbers. It has practical applications in fields such as cryptography and is closely related to prime numbers, as every number can be expressed as a unique combination of prime numbers through prime factorization.
  • #1
PennState666
18
0
Prime Division HELP!

Homework Statement



I need to be able to understand and likely prove that for any positive odd integer n,
8 | (n^2 -1 )

Homework Equations





The Attempt at a Solution


odd can be said to be n = 2k +1
so 8 | (2k + 1)^2 -1
 
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  • #2


Keep going. Now expand out (2k+1)^2 - 1 and collect terms. Then think about the terms in k and k+1.
 
  • #3


I got stumped trying mathematical induction i was hoping for a new approach
 
  • #4


Try the approach that phyzguy is suggesting.
 

1. What is Prime Division?

Prime Division is a mathematical concept that involves dividing a number into its prime factors. This means breaking the number down into its smallest factors that are only divisible by 1 and itself.

2. How do you find the prime factors of a number?

To find the prime factors of a number, you can use a process called prime factorization. This involves dividing the number by its smallest prime factor, and then continuing to divide the resulting numbers by their smallest prime factors until all factors are prime.

3. Why is Prime Division important?

Prime Division is important because it helps us understand the fundamental building blocks of numbers. It also has many practical applications in fields such as cryptography and computer science.

4. Can all numbers be divided into their prime factors?

Yes, all numbers can be divided into their prime factors. However, some numbers may have very large prime factors that are difficult to find without the use of advanced mathematical algorithms.

5. How is Prime Division related to prime numbers?

Prime Division is closely related to prime numbers, as prime numbers are the building blocks of prime factorization. Every number can be expressed as a unique combination of prime numbers through the process of prime factorization.

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