104 Number Theory Problems - From the Training of the USA IMO Team

Cover:

Contents:

1 Foundations of Number Theory

• Divisibility
• Division Algorithm
• Primes
• The Fundamental Theorem of Arithmetic
• G.C.D.
• Euclidean Algorithm
• Bezout’s Identity
• L.C.M.
• The Number of Divisors
• The Sum of Divisors
• Modular Arithmetics
• Residue Classes
  
  
• Fermat’s Little Theorem and Euler’s Theorem
• Euler’s Totient Function
• Multiplicative Function
• Linear Diophantine Equations
• Numerical Systems
• Divisibility Criteria in the Decimal System
• Floor Function
• Legendre’s Function
• Fermat Numbers
• Mersenne Numbers
• Perfect Numbers

2 Introductory Problems
3 Advanced Problems
4 Solutions to Introductory Problems
5 Solutions to Advanced Problems

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