And then you can generalize this to modulo different primes, defining equivalence relations to construct Z _ p from Z, what changes if you compute modulo a number that is not a prime, etc . etc . You can probably go all the way to the proof of the quadratic reciprocity law . talk ) 13 : 27, 14 May 2013 ( UTC)
12.
Note that the quadratic reciprocity law allows one to easily test whether " a " is a nonzero quadratic residue mod " p ", thus we get a practical way to determine which " p "-adic numbers ( for " p " odd ) have a " p "-adic square root, and it can be extended to cover the case " p " = 2 using the more general version of Hensel's lemma ( an example with 2-adic square roots of 17 is given later ).
