Infinitely many insolvable Diophantine equations II
نویسندگان
چکیده
Let f(X1, . . . , Xm) be a quadratic form in m variables X1, . . . , Xm with integer coefficients. Then it is well-known that the Diophantine equation f(X1, . . . , Xm) = 0 has a nontrivial solution in integers if and only if the equation has a nontrivial solution in real numbers and the congruence f(X1, . . . , Xm) ≡ 0 (mod N) has a nontrivial solution for every integer N > 1. Such a principle is called the Hasse principle. In this paper, we explicitly give several types of families of the Diophantine equations of degree two, not homogeneous, for which the Hasse principle fails. 2000 Mathematics Subject Classification: 11D09, 11A07
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