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Switzerland Contests
Switzerland Team Selection Test
2003 Switzerland Team Selection Test
1
x+y = x^3 +y^3 = x^5 +y^5 = a
x+y = x^3 +y^3 = x^5 +y^5 = a
Source: Switzerland - Swiss TST 2003 p1
February 18, 2020
system of equations
parameter
algebra
Problem Statement
Real numbers
x
,
y
,
a
x,y,a
x
,
y
,
a
satisfy the equations
x
+
y
=
x
3
+
y
3
=
x
5
+
y
5
=
a
x+y = x^3 +y^3 = x^5 +y^5 = a
x
+
y
=
x
3
+
y
3
=
x
5
+
y
5
=
a
Find all possible values of
a
a
a
.
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