show that the legendre symbol of y^3 congruent to 2 mod 7 is -1. I know how to work quadratic problems, but cubic is something i have never come across. Any ideas?? I assume you can use the quadratic law of reciprocity, but i have no idea how to go about doing it.
Your problem was not clear. What I wrote above was my interpertation of your problem because of your title "Legendre symbol". There is no such thing as a Legendre symbol for cubic resides, while there is an analouge called the cubic residue symbol.
I happen to think that biquadradic (quartic) is easier.
Maybe it is just because looks nicer than .