Includes bibliographical references (p. 371) and index.

What is number theory? -- Pythagorean triples -- Pythagorean triples and the unit circle -- Sums of higher powers and Fermat's Last Theorem -- Divisibility and the greatest common divisor -- Linear equations and the greatest common divisor -- Factorization and the fundamental theorem of arithmetic -- Congruences -- Congruences, powers, and Fermat's Little Theorem -- Congruences, powers, and Euler's Formula -- Euler's Phi function -- Prime numbers -- Counting primes -- Mersenne primes -- Mersonne primes and perfect numbers -- Powers modulo m and successive squaring -- Computing Kth roots modulo m -- Powers, roots, and "unbreakable" codes -- Euler's phi function and sums of divisors -- Powers modulo p and primitive roots -- Primitive roots and indices -- Squares modulo p -- Is -1 a square modulo p? Is 2? -- Quadratic reciprocity -- Which primes are sums of two squares? -- Which numbers are sums of two squares? -- The equation X⁴ + Y⁴ = Z⁴ -- Square-triangular numbers revisited -- Pell's equation -- Diophantine approximation -- Diophantine approximation and Pell's equation -- Primality testing and Carmichael numbers -- The Gaussian integers and unique factorization -- Irrational numbers and transcendental numbers -- Binomial coefficients and Pascal's triangle -- Fibanacci's rabbits and linear recurrence sequences -- Generating functions -- Sums of powers -- Cubic curves with elliptic curves -- Elliptic curves with few rational points -- Points on elliptic curves modulo p -- Torsion collections modulo p and bad primes -- Defect bounds and modularity patterns -- Elliptic curves and Fermat's last theorem.