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All-Russian Olympiad Regional Round
2003 All-Russian Olympiad Regional Round
8.6
8.6
Part of
2003 All-Russian Olympiad Regional Round
Problems
(1)
a/c = b/d = *ab + 1)/(cd + 1) - All-Russian MO 2003 Regional (R4) 8.6
Source:
9/17/2024
For some natural numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
and
d
d
d
the following equations holds:
a
c
=
b
d
=
a
b
+
1
c
d
+
1
.
\frac{a}{c}= \frac{b}{d}= \frac{ab + 1}{cd + 1} .
c
a
=
d
b
=
c
d
+
1
ab
+
1
.
Prove that
a
=
c
a = c
a
=
c
and
b
=
d
b = d
b
=
d
.
algebra