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Austrian-Polish
2004 Austrian-Polish Competition
5
5
Part of
2004 Austrian-Polish Competition
Problems
(1)
Austria-Poland where the sum is 27 and the product 24
Source: Austria-Poland 2004, single competition, problem 5
2/13/2005
Determine all
n
n
n
for which the system with of equations can be solved in
R
\mathbb{R}
R
:
∑
k
=
1
n
x
k
=
27
\sum^{n}_{k=1} x_k = 27
k
=
1
∑
n
x
k
=
27
and
∏
k
=
1
n
x
k
=
(
3
2
)
24
.
\prod^{n}_{k=1} x_k = \left( \frac{3}{2} \right)^{24}.
k
=
1
∏
n
x
k
=
(
2
3
)
24
.
induction
analytic geometry
algebra unsolved
algebra