The Queen of Mathematics: An Introduction to Number Theory

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Like other introductions to number theory, this text includes the usual curtsy to divisibility theory, the bow to congruence, and the little chat with quadratic reciprocity. It also includes proofs of results such as Lagrange’s Four Square Theorem, the theorem behind Lucas’s test for perfect numbers, the theorem that a regular n-gon is constructible just in case o(n) is a power of 2, the fact that the circle cannot be squared, Dirichlet’s theorem on primes in arithmetic progressions, the Prime Number Theorem and Rademacher’s partition theorem. The proofs of these theorems have been made as elementary as possible. The book includes presentations of palindromic simple continued fractions, an elementary solution of Lucas’s square pyramid problem, Baker’s solution for simultaneous Fermat equations, an elementary proof of Fermat’s polygonal number conjecture, and the Lambek-Moser-Wild theorem.