Using congruences, I seek to prove two things:
1) $x^2 - 4y^2 = 3$ has no solutions in integers $x,y,z$.
I think this can be done using modulo 4? How so?
2) $3x^3 - 7y^3 + 21 z^3 = 2$ has no solutions in integers $x,y,z$.
Not sure how to attack this one...