Chapter 9. Quadratic Congruences

This chapter studies the solution of quadratic congruences for prime p, and . The basic properties of quadratic congruences modulo primes, including the study of the Legendre symbol, are developed in the first section. These lead to Euler's criterion for solvability of the congruence. An efficient algorithm is discussed for the solution of the congruence. The general congruence is solved using these techniques and the Chinese Remainder Theorem.