科研之友
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摘要
Let p be a fixed prime and k be a fixed odd positive integer. Further let N(p(k)) denote the number of pairs of integer points (x,+/- y) on the elliptic curve E : y(2) = x(3) - p(k)x with y > 0. Using some properties of the Diophantine equations, we gave an exact upper bound estimate for N(p(k)). That is, we proved that N(p(k)) <= 4.
