MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2010 National Olympiad First Round
22
22
Part of
2010 National Olympiad First Round
Problems
(1)
Turkey NMO 2010 1st Round - P22 (Number Theory)
Source:
7/27/2012
How many pairs of integers
(
x
,
y
)
(x,y)
(
x
,
y
)
are there such that
x
y
+
7
+
y
x
+
7
=
1
\frac{x}{y+7}+\frac{y}{x+7}=1
y
+
7
x
+
x
+
7
y
=
1
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
18
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
17
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
15
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
14
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
11
<span class='latex-bold'>(A)</span>\ 18 \qquad<span class='latex-bold'>(B)</span>\ 17 \qquad<span class='latex-bold'>(C)</span>\ 15 \qquad<span class='latex-bold'>(D)</span>\ 14 \qquad<span class='latex-bold'>(E)</span>\ 11
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
18
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
17
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
15
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
14
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
11