Birch And Swinnertion-Dyer Part 2

This second paper, which proves 63 theorems, together with the first paper that gives a complete proof of the Birch and Swinnerton-Dyer conjecture, has completed a comprehensive program on the solutions of polynomials over Z and Q\Z in algebra and number theory. “Proof that in infinitely many cases the Birch and Swinnerton-Dyer conjecture has no integer solutions and extend this to polynomials.” Birch and Swinnerton-Dyer conjecture: the solutions of a type-1 Elliptic curve depend on a function L, if L(1) = 0 , the numbers of solutions over Z or Q\Z is infinite, if L(1) ̸ = 0, the number of solutions is finite, the standard form of an Elliptic curve : y2 = x3 + ax +b, with a,b ∈ Q, and 4.a3 + 27.b2 ̸ = 0, Mathematical methods used for this article: proof by Contradiction, Fermat’s Little Theorem, and division remainders,etc (For p prime, ap − a is divisible by p. If (a,p) = 1, then ap−1 − 1 is divisible by p etc)