Additive Number Theory The Classical Bases

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Focusing on classical problems in additive number theory, this book introduces essential analytical and combinatorial methods, particularly the circle and sieve methods. Aimed at students rather than experts, it emphasizes clarity by including detailed proofs that may seem obvious. Key concepts include Lagrange's theorem, which states that every nonnegative integer can be expressed as the sum of four squares, and explores various additive bases, such as squares and primes, alongside classical questions like Waring's problem and the Goldbach conjecture.