Affiliation:
1. School of Mathematics and Statistics, North China University of Water Resources and Electric Power , Zhengzhou , 450046 , People’s Republic of China
2. School of Mathematics and Information Sciences, Henan University of Economics and Law , Zhengzhou , 450000 , People’s Republic of China
Abstract
Abstract
In this paper, we show that if
λ
1
,
λ
2
,
λ
3
{\lambda }_{1},{\lambda }_{2},{\lambda }_{3}
are non-zero real numbers, and at least one of the numbers
λ
1
,
λ
2
,
λ
3
{\lambda }_{1},{\lambda }_{2},{\lambda }_{3}
is irrational, then the integer parts of
λ
1
n
1
2
+
λ
2
n
2
3
+
λ
3
n
3
4
{\lambda }_{1}{n}_{1}^{2}+{\lambda }_{2}{n}_{2}^{3}+{\lambda }_{3}{n}_{3}^{4}
are prime infinitely often for integers
n
1
,
n
2
,
n
3
{n}_{1},{n}_{2},{n}_{3}
. This gives an improvement of an earlier result.
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