证明了:如果η是实数, λ1,μ1,μ2,μ3,μ4,θ1,θ2是非零实数,并且不同一符号,至少有一个λ1/μj (i=1,2,3,4)是无理数, 那么对任意0<σ<1/30,不等式|λ1x21+μ1x32+μ2x33+μ3x34+μ4x35+θ1x46+θ2x57+η|<(max|xi|)-σ有无穷多整数解x1,...,x7.%It is proved that: let η be real, let λ1,μ1,μ2,μ3,μ4,θ1,θ2 be nonzero real numbers, not all of the same sign, such that at least one ratio λ1/μi (i=1,2,3,4) is irrational, then for any 0<σ<1/30, the inequality|λ1x21+μ1x32+μ2x33+μ3x34+μ4x35+θ1x46+θ2x57+η|<(max|xi|)-σhas infinitely many solutions in integers x1,...,x11.
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