MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2013 National Olympiad First Round
30
30
Part of
2013 National Olympiad First Round
Problems
(1)
P30 [Number Theory] - Turkish NMO 1st Round - 2013
Source:
4/18/2013
For how many postive integers
n
n
n
less than
2013
2013
2013
, does
p
2
+
p
+
1
p^2+p+1
p
2
+
p
+
1
divide
n
n
n
where
p
p
p
is the least prime divisor of
n
n
n
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
212
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
206
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
191
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
185
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
173
<span class='latex-bold'>(A)</span>\ 212 \qquad<span class='latex-bold'>(B)</span>\ 206 \qquad<span class='latex-bold'>(C)</span>\ 191 \qquad<span class='latex-bold'>(D)</span>\ 185 \qquad<span class='latex-bold'>(E)</span>\ 173
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
212
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
206
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
191
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
185
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
173
modular arithmetic