Simple Proof Check - Number Theory

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In summary, the conversation discusses a proof related to number theory and the use of prime factorization. The person is seeking feedback on their proof and their use of a pattern to justify their reasoning. They are advised to use the concept of unique prime factorization and explain why square numbers have only even exponents in their prime factorization to further support their logic.
  • #1
Fisicks
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Recently I've stumbled upon number theory and decided to order a book which is coming soon so in the mean time I've decided to try what looked like an easy proof to kinda practice on. So tell me where my logic fails or where it surprisingly doesn't. criticism appreciated.

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  • #2
The "investigate" line doesn't justify why
n^2/6 = 6k^2
which is the crux of the proof.
 
  • #3
well i just found a pattern, and it holds.

ex. the 15th natural number squared divisible by 6 is 8100. So K is 15, and you have
8100/6=6*15^2
1350=1350
 
  • #4
Can someone give me more insight on what greathouse said, and how to salvage this proof? Its not like n^2/6=6k^2 isn't true for my conditions.
 
  • #5
Fisicks said:
Can someone give me more insight on what greathouse said, and how to salvage this proof? Its not like n^2/6=6k^2 isn't true for my conditions.

try every integer has a unique prime factorization and represent a number divisible by 6 as a product of its prime factors. explain why square numbers have only even exponents in their prime factorization. Use these to justify your logic.
 

1. What is number theory?

Number theory is a branch of mathematics that deals with the properties and relationships of numbers, particularly integers. It involves studying patterns and structures in numbers, as well as their properties and applications.

2. What is a simple proof check?

A simple proof check is a process of verifying the validity and correctness of a mathematical proof. It involves carefully examining the logical steps and assumptions used in the proof to ensure that it is sound and free from errors.

3. Why is number theory important?

Number theory has many real-world applications, such as in cryptography, coding theory, and computer science. It also helps to understand the fundamental properties of numbers and serves as the foundation for other branches of mathematics.

4. How can I check the validity of a proof in number theory?

To check the validity of a proof in number theory, you can follow a systematic approach that involves carefully examining each logical step, checking for any errors or incorrect assumptions, and making sure that the conclusion follows logically from the premises.

5. What are some common mistakes to watch out for when checking a proof in number theory?

Some common mistakes to watch out for when checking a proof in number theory include incorrect use of mathematical notation, logical fallacies, and incorrect assumptions or claims. It is also important to check for any errors in calculations or algebraic manipulations.

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