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Kvant 2019
M2585
M2585
Part of
Kvant 2019
Problems
(1)
Sum of odd powers is 0
Source: Kvant Magazine No. 11 2019 M2585*
3/14/2023
Let
a
1
,
.
.
.
,
a
n
a_1,...,a_n
a
1
,
...
,
a
n
be
n
n
n
real numbers. If for each odd positive integer
k
⩽
n
k\leqslant n
k
⩽
n
we have
a
1
k
+
a
2
k
+
…
+
a
n
k
=
0
a_1^k+a_2^k+\ldots+a_n^k=0
a
1
k
+
a
2
k
+
…
+
a
n
k
=
0
, then for each odd positive integer
k
k
k
we have
a
1
k
+
a
2
k
+
…
+
a
n
k
=
0
a_1^k+a_2^k+\ldots+a_n^k=0
a
1
k
+
a
2
k
+
…
+
a
n
k
=
0
.Proposed by M. Didin
algebra
Polynomials
Kvant