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MathLinks Contest 4th
5.3
0453 number theory 4th edition Round 5 p3
0453 number theory 4th edition Round 5 p3
Source:
May 7, 2021
number theory
4th edition
Problem Statement
The sequence
{
x
n
}
n
\{x_n\}_n
{
x
n
}
n
is defined as follows:
x
1
=
0
x_1 = 0
x
1
=
0
, and for all
n
≥
1
n \ge 1
n
≥
1
(
n
+
1
)
3
x
n
+
1
=
2
n
2
(
2
n
+
1
)
x
n
+
2
(
3
n
+
1
)
.
(n + 1)^3 x_{n+1} = 2n^2 (2n + 1)x_n + 2(3n + 1).
(
n
+
1
)
3
x
n
+
1
=
2
n
2
(
2
n
+
1
)
x
n
+
2
(
3
n
+
1
)
.
Prove that
{
x
n
}
n
\{x_n\}_n
{
x
n
}
n
contains infinitely many integer numbers.
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