一个加性混合幂丢番图不等式Ⅲ(英文)

One Additive Diophantine Inequality with Mixed Powers

证明了:如果λ1,…,λ11,μ是非零实数,并且不同一符号,至少有一个λi/λj是无理数,那么对任意实数η和ε>0,不等式λ1x14+…+λ11x141+μy2+η<ε有无穷多正整数解x1,…,x11,y.

In this paper, it is shown that., if λ1 ,…,λ11, μ are non-zero real numbers, not all of the same sign, such that at least one ratio λ/λi is irrational, then for any real number η and ε〉0 the inequality ｜λ1x1^4＋…＋λ11x11^4＋μy^2＋η｜｜〈ε has infinitely many solutions in positive integers x1,… ,x11,y.