800000007 is 7(mod 8).
x^2, y^2 and z^2 can be 0,1,4(mod 8).
we can never get 7(mod 8) from them. :)
10511 is 3(mod 4).
a^2 and b^2 can be 0,1(mod 4).
again we can't get that..
the question should be that these don't have integral solutions...
last one has a solution, y = 0. x = root3.
i should have written.
y = 0, x = + , - root3.
x^2 + 7y^2 > 3. for all x , y = integers, and both x and y not simultaneously 0.
and if y = 0, x not equal to + 1 , - 1.
we can check these cases by hand.
like to kar de bhai!!