MathDB
Problems
Contests
National and Regional Contests
Poland Contests
Poland - Second Round
1953 Poland - Second Round
4
x_k x_{k+1} = k, nxn system
x_k x_{k+1} = k, nxn system
Source: Polish MO second round 1953 p4
August 29, 2024
algebra
system of equations
Problem Statement
Solve the system of equations
<
b
r
/
>
<
b
r
/
>
x
1
x
2
=
1
<
b
r
/
>
x
2
x
3
=
2
<
b
r
/
>
x
3
x
4
=
3
<
b
r
/
>
…
<
b
r
/
>
x
n
x
1
=
n
<
b
r
/
>
\qquad<br /> \begin{array}{c}<br /> x_1x_2 = 1\\<br /> x_2x_3 = 2\\<br /> x_3x_4 = 3\\<br /> \ldots\\<br /> x_nx_1 = n<br /> \end{array}
<
b
r
/
>
<
b
r
/
>
x
1
x
2
=
1
<
b
r
/
>
x
2
x
3
=
2
<
b
r
/
>
x
3
x
4
=
3
<
b
r
/
>
…
<
b
r
/
>
x
n
x
1
=
n
<
b
r
/
>
Back to Problems
View on AoPS