An Introduction to the Theory of Numbers

a₁ a²+b² absolutely convergent algebraic integer algebraic number algorithm an+1 approximation arithmetic b₁ coefficients congruence contradiction coprime corresponding cubes D. H. Lehmer decimal deduce defined digits divisible equation equivalent Euclid's Euclid's algorithm Euclidean Euler example Fermat's theorem follows formulae function fundamental theorem Gaussian integers highest common divisor In+1 infinity integers of k(p integral polynomial integral quaternions interval irrational Journal London Math Landau loglog mod p² modulus multiple non-residue NOTES ON CHAPTER odd prime P₁ particular partitions positive integers prime factors problem proof of Theorem properties prove Theorem quadratic fields quadratic residue quotients rational integers rational primes representation roots satisfies sequence simple continued fraction solution square suppose Theorem 369 theory of numbers transcendental trivial true unity values Wilson's theorem Wolstenholme's theorem write x₁ y₁