EGINNING A PROOF: Proving 2n-1 is Prime for all n

  • Thread starter brad sue
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In summary, the purpose of proving 2n-1 is prime for all n is to demonstrate its truth and its significance in number theory. A prime number is a positive integer that is divisible by only 1 and itself, making it a fundamental building block of all other whole numbers. The first step in beginning a proof is to clearly state the theorem and define any unfamiliar terms. The general approach to proving 2n-1 is prime for all n is to use a proof by contradiction, which confidently concludes the statement's truth for all values of n. This proof technique is important as it leaves no other possible solution or outcome.
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brad sue
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Hi I have difficulty to begin with this problem:

prove or disapprove that 2n-1 is prime for all non negative integers n.

I know the definition of a prime number but how to apply it for this proof?

Please, can I have a suggestion to start this problem?

B
 
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Try some values of n and see if you can find a composite number (hint: I wouldn't be telling you to do this unless your search would end eventually).
 

1. What is the purpose of proving 2n-1 is prime for all n?

The purpose of this proof is to demonstrate the truth of the statement that 2n-1 is always a prime number for any value of n. It is an important concept in number theory and can aid in solving other mathematical problems.

2. What is a prime number?

A prime number is a positive integer that is divisible by only 1 and itself. This means that it has exactly two factors, making it a fundamental building block of all other whole numbers.

3. How do you begin a proof?

The first step in beginning a proof is to clearly state the theorem or statement that you are trying to prove. Next, you should define any terms or concepts that may be unfamiliar. This is followed by a list of assumptions or given information, which will serve as the foundation for your proof.

4. What is the general approach to proving 2n-1 is prime for all n?

The general approach to proving this statement is to use a proof by contradiction. This means assuming that the statement is false and then using logical reasoning and mathematical operations to show that this leads to a contradiction. This contradiction proves that the original statement must be true.

5. Why is it important to use a proof by contradiction in this case?

A proof by contradiction is important in this case because it allows us to show that there is no other possible solution or outcome. By assuming the statement is false and showing that it leads to a contradiction, we can confidently conclude that the statement must be true for all values of n.

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