Affiliation:
1. Faculty of Applied Mathematics and Informatics , Technical University of Sofia , 8, St. Kliment Ohridski Blvd., 1756 Sofia , Bulgaria
Abstract
Abstract
Let
[
⋅
]
{[\,\cdot\,]}
be the floor function.
In this paper, we prove that if
1
<
c
<
16559
15276
{1<c<\frac{16559}{15276}}
, then
every sufficiently large positive integer N can be represented in the form
N
=
[
p
1
c
]
+
[
p
2
c
]
+
[
p
3
c
]
,
N=[p^{c}_{1}]+[p^{c}_{2}]+[p^{c}_{3}],
where
p
1
,
p
2
,
p
3
{p_{1},p_{2},p_{3}}
are primes, such that
p
1
=
x
2
+
y
2
+
1
{p_{1}=x^{2}+y^{2}+1}
.
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