## The Theory of Numbers |

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a=b mod Alexander Macfarlane arithmetic progression belongs modulo chapter common factor common prime factor congruence ax=c mod congruent modulo COrOllary Definition denote different from zero different primes Diophantine equations divisible by p2 ELEMENTARY PROPERTIES Eratosthenes Euler's criterion evidently EXERCISES exist integers exist primitive roots exists an integer exponent dt Fermat's general theorem finite number following theorem follows at once fundamental theorem greatest common divisor gruence Hence the number highest power hypothesis integers less integers not greater irreducible fractions least common multiple necessary and sufficient notation number of integers number of primes numerical right triangle obtained obviously odd prime number pip2 positive integers primitive root modulo proof PROPERTIES OF CONGRUENCES prove the following quadratic character quadratic non-residue modulo quadratic residue modulo ratic relatively prime integers second member simple Fermat theorem solution square number suppose theorem follows theory of numbers tion whence Wilson's Theorem X-root