关于丢番图方程x^3±3~9＝Dy^2

给出了方程ｘ~３±３~９＝Ｄｙ~２的全部非平凡整数解，其中Ｄ＞０，无平方因子，且不能被６ｋ＋１型的素数整除。

Diophantine Approximation with Four Squares of Primes and Powers of Two

Under certain condition, the inequality |λ_1p_1~2+λ_2p_2~2+λ_3p_3~2+λ_4p_4~2+μ_12^(x1)+…+μ_s2^(xs)+γ|＜ηhas infinitely many solutions in primes p_1,p_2,p_3,p_4 and positive integers x_1,…,x_s.