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Austrian-Polish
1979 Austrian-Polish Competition
6
6
Part of
1979 Austrian-Polish Competition
Problems
(1)
system of equations \sum_{i=1}^{n} x_i^k= a^k
Source: Austrian Polish 1979 APMC
4/26/2020
A positive integer
n
n
n
and a real number
a
a
a
are given. Find all
n
n
n
-tuples
(
x
1
,
.
.
.
,
x
n
)
(x_1, ... ,x_n)
(
x
1
,
...
,
x
n
)
of real numbers that satisfy the system of equations
∑
i
=
1
n
x
i
k
=
a
k
f
o
r
k
=
1
,
2
,
.
.
.
,
n
\sum_{i=1}^{n} x_i^k= a^k \,\,\,\, for \,\,\,\, k = 1,2, ... ,n
i
=
1
∑
n
x
i
k
=
a
k
f
or
k
=
1
,
2
,
...
,
n
algebra
system of equations