关于不定方程x^3+5~3=2Ry^2

On the indefinite equation x^3+5~3=2Ry^2

设R=p1 p2 Q,Q=r i(n∈Z),ri-1(mod6)(1≤i≤n)为互异的奇素数,p1≡p2≡1(mod 6)为奇素数。运用初等方法得出了不定方程x 3+53=2Ry 2无正整数解的一个充分条件。

LetR =p1 p2 Q,Q= r i(n∈ Z+),p1 ≡p2 ≡1(mod 6), ri =1(mod 6)(1 ≤i ≤n) be different odd primes, p1, p2 be odd primes. One sufficient condition is obtained that the equation in title has no positive integer with the help of elementary method.