Quadratic Residues and the Quadratic Reciprocity Law
Part of the Undergraduate Texts in Mathematics book series (UTM)
As shown in Chapter 5, the problem of solving a polynomial congruencewhere p is an odd prime and (mod p). Since the modulus is prime we know that (1) has at most two solutions. Moreover, if x is a solution so is − x, hence the number of solutions is either 0 or 2.
can be reduced to polynomial congruences with prime moduli plus a set of linear congruences. This chapter is concerned with quadratic congruences of the form
KeywordsDiophantine Equation Quadratic Residue Multiplicative Property Legendre Symbol Linear Congruence
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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