## Elementary Theory of NumbersThis book explains clearly and in detail the basic concepts and methods of calculations of the elementary theory of numbers. It consists of 7 chapters illustrated by numerous examples and exercises. Answers together with some hints to the exercises are given at the end of the book. It may be used as a textbook for undergraduate students. |

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algebraic integer algebraic number theory complete residue system completes the proof congruence x2 congruent modulo conjecture different solutions digits discuss divided Euler Evidently Exercise exist Fermat number following theorem g P g Gauss given congruence given equation Goldbach's conjecture greatest common divisor Hence the theorem incongruent modulo indeterminate equation infinitely Jacobi symbol least common multiple least positive Legendre symbol Mersenne numbers method mod 2k mod p2 mod q modp necessary and sufficient number of integers number of solutions obtain odd integer odd number odd prime factors perfect number positive divisors positive integer solution prime divisor prime number primitive root problem quadratic nonresidue quadratic residue real number reduced residue system relatively prime required solution residue system modulo second degree Show Similarly solution of x2 solutions of f(x solving the congruence square number sufficient condition system of congruences theorem is proved Wilson's theorem