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2022 CMIMC
1.7
2022 Alg/NT Div 1 P7
2022 Alg/NT Div 1 P7
Source:
February 28, 2022
algebra
number theory
Problem Statement
Let
f
(
n
)
f(n)
f
(
n
)
count the number of values
0
≤
k
≤
n
2
0\le k\le n^2
0
≤
k
≤
n
2
such that
43
∤
(
n
2
k
)
43\nmid\binom{n^2}{k}
43
∤
(
k
n
2
)
. Find the least positive value of
n
n
n
such that
4
3
43
∣
f
(
4
3
n
−
1
42
)
43^{43}\mid f\left(\frac{43^{n}-1}{42}\right)
4
3
43
∣
f
(
42
4
3
n
−
1
)
Proposed by Adam Bertelli
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