【摘要】 本文用初等方法研究了丢番图方程x~3±8=3Dy~2,首先补充了柯召等的结果,其次给出D含6k+1型素因子时无正数解的一些充分性条件．更多还原

【Abstract】 For the diophantine equationx3±8=3Dy2 (l±)In this paper, We prove the following theorems:Theorem 1 let D = p1, s>l, pi (i= l, 2,…, s) are dissimilar primes, then whenl) Pi≡ll, l7 (mod24), i= l, 2, …, s; or 2) pi=5, 23 (mod24), i= l, 2,…, s, the equations (l±) all has no solutions in positive integer.Theorem 2 let D = pi, s>2, pi (i= l, 2,…, s) are dissimilar primes, if there isi=lj∈{2, ..., s}, so that () = -l. then when l) pi≡7, l3 (mod24), pi≡5(mod6), i= 2, ..., s; or 2) pl≡ l (mod6), pi≡5 (mod6), i= 2,…, s, for theequation (l+) D≡l (mod4), for the equation (l-) D≡3 (mod4), the equations (1± ) all has no solutions in positive integer.更多还原