Help for Number Theory problem

Thread starter dessy
Start date Oct 14, 2007
Tags

Number theory Theory

In summary, when approaching a difficult Number Theory problem, it is important to understand the question and constraints, break down the problem into smaller parts, and utilize known theorems and techniques. There is no specific method for solving these problems, but some commonly used techniques include proof by contradiction, mathematical induction, and modular arithmetic. Calculators or computers are typically not necessary for solving Number Theory problems, but can be helpful for checking solutions. Resources for learning about Number Theory include textbooks, online courses, and video lectures, and improving problem-solving skills can be achieved through practice, reading about techniques, and collaborating with others.

Oct 14, 2007

dessy

Prove that 1/5*n^5+1/3*n^3+7/15*n is an integer for all integers n.

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Oct 14, 2007

morphism

Science Advisor

Homework Helper

Look at 3n^5 + 5n^3 + 7n mod 5 and mod 3.

Oct 14, 2007

dessy

Thanks, Morphism

1. How can I approach a difficult Number Theory problem?

When facing a challenging Number Theory problem, it is important to first understand the question and any given constraints. Then, try to break down the problem into smaller, more manageable parts. Utilizing known theorems and techniques can also be helpful in finding a solution. Don't be afraid to experiment and try different approaches.

2. Is there a specific method for solving Number Theory problems?

There is no one method for solving Number Theory problems, as each problem is unique and may require a different approach. However, some commonly used techniques in Number Theory include proof by contradiction, mathematical induction, and modular arithmetic.

3. Can I use a calculator or computer to solve Number Theory problems?

In most cases, a calculator or computer is not necessary for solving Number Theory problems. These problems usually involve logical reasoning and mathematical concepts rather than numerical calculations. However, technology can be helpful for checking solutions or conducting experiments.

4. What are some helpful resources for learning about Number Theory?

There are many resources available for learning about Number Theory, including textbooks, online courses, and video lectures. Some popular books on the subject include "Introduction to Analytic Number Theory" by Tom Apostol and "Number Theory: A Lively Introduction with Proofs, Applications, and Stories" by James Pommersheim, Tim Marks, and Erica Flapan.

5. How can I improve my problem-solving skills in Number Theory?

Practicing and solving various Number Theory problems is the best way to improve problem-solving skills in this field. Additionally, reading about different techniques and approaches used in Number Theory can expand one's problem-solving toolkit. Collaborating with others and discussing solutions can also be beneficial.