09-15-2026, 12:59 AM
Elementary Number Theory in Nine Chapters by James J. Tattersall is designed as a one-semester introduction to elementary number theory, combining mathematical development with historical context. The book begins with natural numbers, polygonal numbers, sequences, and mathematical induction, then develops the fundamental ideas of divisibility, greatest common divisors, the Euclidean algorithm, Pythagorean triples, prime numbers, factorization, and arithmetic functions. It then moves to perfect and amicable numbers and, importantly, modular arithmetic, including congruences, Euler's $\phi$-function, and congruences of higher degree.
The later chapters broaden the subject toward both classical and modern applications: cryptology, including classical ciphers and exponential/RSA-type ideas; representations of integers as sums of squares; Pell's equation; binary quadratic forms; continued fractions; $p$-adic analysis; and finally partitions and generating functions, including the Pentagonal Number Theorem.
The book emphasizes the contributions of mathematicians such as Euclid, Fermat, Gauss, Legendre, and Euler, and contains a large collection of exercises—the second edition added nearly 400 new problems. Overall, it is a broad, historically motivated introduction that is particularly suitable for someone wanting to move from elementary arithmetic toward serious number-theoretic problem solving.
BOOK
The later chapters broaden the subject toward both classical and modern applications: cryptology, including classical ciphers and exponential/RSA-type ideas; representations of integers as sums of squares; Pell's equation; binary quadratic forms; continued fractions; $p$-adic analysis; and finally partitions and generating functions, including the Pentagonal Number Theorem.
The book emphasizes the contributions of mathematicians such as Euclid, Fermat, Gauss, Legendre, and Euler, and contains a large collection of exercises—the second edition added nearly 400 new problems. Overall, it is a broad, historically motivated introduction that is particularly suitable for someone wanting to move from elementary arithmetic toward serious number-theoretic problem solving.
BOOK
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