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MathLinks Contest 2nd
2.2
0222 number theory 2nd edition Round 2 p2
0222 number theory 2nd edition Round 2 p2
Source:
May 10, 2021
number theory
2nd edition
Problem Statement
Let
{
a
n
}
n
≥
0
\{a_n\}_{n\ge 0}
{
a
n
}
n
≥
0
be a sequence of rational numbers given by
a
0
=
a
1
=
a
2
=
a
3
=
1
a_0 = a_1 = a_2 = a_3 = 1
a
0
=
a
1
=
a
2
=
a
3
=
1
and for all
n
≥
4
n \ge 4
n
≥
4
we have
a
n
−
4
a
n
=
a
n
−
3
a
n
−
1
+
a
n
−
2
2
a_{n-4}a_n = a_{n-3}a_{n-1} + a^2_{n-2}
a
n
−
4
a
n
=
a
n
−
3
a
n
−
1
+
a
n
−
2
2
. Prove that all the terms of the sequence are integers.
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