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Romania TST 2016 Day 1 P4
Romania TST 2016 Day 1 P4
Source: Romania TST 2016 Day 1 P4
November 1, 2017
number theory
Problem Statement
Determine the integers
k
≥
2
k\geq 2
k
≥
2
for which the sequence
{
(
2
n
n
)
(
m
o
d
k
)
}
n
∈
Z
≥
0
\Big\{ \binom{2n}{n} \pmod{k}\Big\}_{n\in \mathbb{Z}_{\geq 0}}
{
(
n
2
n
)
(
mod
k
)
}
n
∈
Z
≥
0
is eventually periodic.
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