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1987 IMO Longlists
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IMO LongList 1987 - Find y (Proposed by Turkey)
IMO LongList 1987 - Find y (Proposed by Turkey)
Source:
September 6, 2010
number theory proposed
number theory
Problem Statement
It is given that
x
=
ā
2272
x = -2272
x
=
ā
2272
,
y
=
1
0
3
+
1
0
2
c
+
10
b
+
a
y = 10^3+10^2c+10b+a
y
=
1
0
3
+
1
0
2
c
+
10
b
+
a
, and
z
=
1
z = 1
z
=
1
satisfy the equation
a
x
+
b
y
+
c
z
=
1
ax + by + cz = 1
a
x
+
b
y
+
cz
=
1
, where
a
,
b
,
c
a, b, c
a
,
b
,
c
are positive integers with
a
<
b
<
c
a < b < c
a
<
b
<
c
. Find
y
.
y.
y
.
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