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Feb13-12, 11:09 AM
P: 144
Hi, I havnt checked the details, but such problems screem for the use of the determinant formed by the x's and y's, and can then also be generalized immediately. I guess the condition is that this determinant has no prime factors, that is being 1 or -1. Any prime factor p would allow a nontrivial relation ax+by=0 over F_p, which then lifts to show a relation with gcd(z_1,z_2)=p. Tell me if that works out.