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