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# Level 3 Number Theory & Algebra

Please, What are the subjects in Math that are needed in a student in Level 3 Nuber Theory ?

Note by Ahmed Taha
4 years, 4 months ago

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The Subject:Maths

The Subject within Maths required for number Theory : Number Theory · 4 years, 4 months ago

Yep but Number Theory has wide elements ! · 4 years, 4 months ago

Sorry i shoud have said sub-subjects precisly · 4 years, 4 months ago

Well you can see the chapters of Elementary Number Theory by David M. Burton. and Problem Solving Strategies by Arthur Engel, though the later is not specially for number theory. There are topics like:

1. GCD, LCM, divisibility( You should be thorough with it)

2. Prime numbers( Their properties)

3. Modulo Arithmetic( Fermat's Theorem, Euler's Theorem, etc.)

4. Functions related to number Theory(Like the number of divisors, or the sum of the divisors of a number)

5. Primitive roots (Perhaps not needed for Level 3)

6. Quadratic Reciprocity (Only the basics)

7. Expressing integers as sums of squares, cubes, etc.

8. Sequences and series (Includes Fibonacci series, recurrence relations, etc.)

9. Integer solutions to equations, Polynomial with Integral coefficients( I am not really sure whether this is algebra or number theory).

10. Mathematical Induction, Well Ordering Principle, Pigeonhole Principle( Though this is combinatorics, it might come in handy)

· 4 years, 4 months ago