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JBMO TST - Turkey
2024 JBMO TST - Turkey
3
Strange question with positive reals
Strange question with positive reals
Source: Turkey JBMO TST 2024 P3
May 13, 2024
algebra
Problem Statement
Find all
x
,
y
,
z
ā
R
+
x,y,z \in R^+
x
,
y
,
z
ā
R
+
such that the sets
(
23
x
+
24
y
+
25
z
,
23
y
+
24
z
+
25
x
,
23
z
+
24
x
+
25
y
)
(23x+24y+25z,23y+24z+25x,23z+24x+25y)
(
23
x
+
24
y
+
25
z
,
23
y
+
24
z
+
25
x
,
23
z
+
24
x
+
25
y
)
and
(
x
5
+
y
5
,
y
5
+
z
5
,
z
5
+
x
5
)
(x^5+y^5,y^5+z^5,z^5+x^5)
(
x
5
+
y
5
,
y
5
+
z
5
,
z
5
+
x
5
)
are same
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