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Kvant 2019
M2572
M2572
Part of
Kvant 2019
Problems
(1)
Sequence of binomial coefficients modulo 2^k
Source: Kvant Magazine No. 8 2019 M2572
3/14/2023
Let
k
k
k
be a fixed positive integer. Prove that the sequence
(
2
1
)
,
(
4
2
)
,
(
8
4
)
,
…
,
(
2
n
+
1
2
n
)
,
…
\binom{2}{1},\binom{4}{2},\binom{8}{4},\ldots, \binom{2^{n+1}}{2^n},\ldots
(
1
2
)
,
(
2
4
)
,
(
4
8
)
,
…
,
(
2
n
2
n
+
1
)
,
…
is eventually constant modulo
2
k
2^k
2
k
.Proposed by V. Rastorguyev
number theory
binomial coefficients
Kvant