Lectures on the Theory of Numbers: New York University, 1951-1952 |
Contents
The Unique Factorization Theorem | 7 |
Arithmetic Functions | 13 |
The Euler Function 9n | 18 |
9 other sections not shown
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2x log a₁ arithmetic functions arithmetic progression characters modulo Chinese Remainder Theorem clearly consider the following contradiction Corollary d-th power residues Definition 1.1 divide divisible divisor estimate finite number fixed modulus following theorem follows immediately Froof induction inversion formula Jacobi symbol Legendre symbol Lemma log g(n log log x₁)² log n log log n n<x log² log²x Lomma m₁ m₂ mn<x modulo 2p n<x A(n n<x n n<x n<x nɛS number of integers number of primes number of solutions O(log odd prime polynomial congruence prime number theorem primitive root modulo progression of length Proof properties prove the theorem quadratic residue reduced residue system relatively prime residue classes roots of unity solutions modulo square free Suppose term Theorem 2.1 unique factorization theorem unique solution vectors write X₁(n Σ Σ