数学杂志
數學雜誌
수학잡지
JOURNAL OF MATHEMATICS
2010年
6期
991-1000
,共10页
孪生素数椭圆曲线%非平凡整数点%Diophantine方程
孿生素數橢圓麯線%非平凡整數點%Diophantine方程
련생소수타원곡선%비평범정수점%Diophantine방정
twin primes elliptic curve%non-trivial integral point%diophantine equation
设p和q是孪生素数.本文讨论了椭圆曲线E_上的非平凡整数点.运用初等数论方法证明了该椭圆曲线至多有1组非平凡整数点(x,±y).
設p和q是孿生素數.本文討論瞭橢圓麯線E_上的非平凡整數點.運用初等數論方法證明瞭該橢圓麯線至多有1組非平凡整數點(x,±y).
설p화q시련생소수.본문토론료타원곡선E_상적비평범정수점.운용초등수론방법증명료해타원곡선지다유1조비평범정수점(x,±y).
In this article,let p and q be twin primes,the non-trivial integral points on the elliptic curve E_:y2 = x(x-p)(x-q) are discussed.Using elementary number theory methods,we prove that this elliptic curve has at most one pair of non-trivial integral points(x,±y).
