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Moscow Mathematical Olympiad
1954 Moscow Mathematical Olympiad
266
MMO 266 Moscow MO 1954 system x(1-1/2^n)+y(1-1/(2^{n+1}))+...
MMO 266 Moscow MO 1954 system x(1-1/2^n)+y(1-1/(2^{n+1}))+...
Source:
August 13, 2019
system of equations
algebra
Problem Statement
Find all solutions of the system consisting of
3
3
3
equations:
x
(
1
−
1
2
n
)
+
y
(
1
−
1
2
n
+
1
)
+
z
(
1
−
1
2
n
+
2
)
=
0
x \left(1 - \frac{1}{2^n}\right) +y \left(1 - \frac{1}{2^{n+1}}\right) +z \left(1 - \frac{1}{2^{n+2}}\right) = 0
x
(
1
−
2
n
1
)
+
y
(
1
−
2
n
+
1
1
)
+
z
(
1
−
2
n
+
2
1
)
=
0
for
n
=
1
,
2
,
3
n = 1, 2, 3
n
=
1
,
2
,
3
.
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