MathDB
Problems
Contests
International Contests
Cono Sur Olympiad
2012 Cono Sur Olympiad
3
3
Part of
2012 Cono Sur Olympiad
Problems
(1)
Cono Sur Olympiad 2012
Source: Problem 3
11/3/2012
3. Show that there do not exist positive integers
a
a
a
,
b
b
b
,
c
c
c
and
d
d
d
, pairwise co-prime, such that
a
b
+
c
d
ab+cd
ab
+
c
d
,
a
c
+
b
d
ac+bd
a
c
+
b
d
and
a
d
+
b
c
ad+bc
a
d
+
b
c
are odd divisors of the number
(
a
+
b
−
c
−
d
)
(
a
−
b
+
c
−
d
)
(
a
−
b
−
c
+
d
)
(a+b-c-d)(a-b+c-d)(a-b-c+d)
(
a
+
b
−
c
−
d
)
(
a
−
b
+
c
−
d
)
(
a
−
b
−
c
+
d
)
.
symmetry
number theory
relatively prime
number theory proposed