一个加性混合幂丢番图不等式(Ⅰ)

One Additive Diophantine Inequality with Mixed Powers (Ⅰ)

本文证明了:如果λ1,…,λ6是非零实数,并且不同一符号,至少有一个λi/j(1≤i,j≤3) 是无理数,那么对任意实数η和ε>0,不等式|λ1x12+λ2x22+λ3x32+λ4s44+λ5x54+λ6x64+η|<ε有无穷多正整数解x1,…,x6．

This paper shows that： if λ1,…,λ6 are nonzero real numbers, not all of the same sign, such that at least one of the ratios λi/λj（1≤i,j≤3） is irrational, then for any real number η and any ε 〉 0, the inequality ｜λ1x1^2＋λ2x2^1＋λ^3x3^2＋λ^4x4^4＋λ^5x5^4-λ6x6^4＋η｜〈ε has infinitely many solutions in positive integers x1,... , x6.