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Polish MO Finals
1956 Polish MO Finals
2
1/ a^n + 1/ b^n+ 1/c ^n =1/ (a^n + b^n + c^n)
1/ a^n + 1/ b^n+ 1/c ^n =1/ (a^n + b^n + c^n)
Source: Polish MO Finals 1956 p2
August 29, 2024
algebra
Problem Statement
Prove that if
1
a
+
1
b
+
1
c
=
1
a
+
b
+
c
\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{1}{a + b + c}
a
1
+
b
1
+
c
1
=
a
+
b
+
c
1
and
n
n
n
is any odd natural number, then
1
a
n
+
1
b
n
+
1
c
n
=
1
a
n
+
b
n
+
c
n
\frac{1}{a^n} + \frac{1}{b^n} + \frac{1}{c^n} =\frac{1}{a^n + b^n + c^n}
a
n
1
+
b
n
1
+
c
n
1
=
a
n
+
b
n
+
c
n
1
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