Here are few resources for learning number theory for competitive programming.

Online resources:

1. Stanford Course: CS 97SI: Introduction to Competitive Programming Contests

2. Codechef: Basic Number Theory Every Programmer Should Know..

3. Topcoder: Primality Testing: Non Deterministic Algorithms

4. Topcoder: Prime Numbers, Factorization and Euler Function

5. MAXimal Russian Site. Contains the implementations of all major algorithms used in competitive programming contests

Books:

1. Elementary Number Theory by David Burton

2. Number Theory for Computing

Online resources:

1. Stanford Course: CS 97SI: Introduction to Competitive Programming Contests

2. Codechef: Basic Number Theory Every Programmer Should Know..

3. Topcoder: Primality Testing: Non Deterministic Algorithms

4. Topcoder: Prime Numbers, Factorization and Euler Function

5. MAXimal Russian Site. Contains the implementations of all major algorithms used in competitive programming contests

Books:

1. Elementary Number Theory by David Burton

**Description**: Elementary Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research. Written in David Burton’s engaging style, Elementary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.2. Number Theory for Computing

**Description**: This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made
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