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Putnam
2018 Putnam
B3
Putnam 2018 B3
Putnam 2018 B3
Source:
December 2, 2018
Putnam
Putnam 2018
Problem Statement
Find all positive integers
n
<
1
0
100
n < 10^{100}
n
<
1
0
100
for which simultaneously
n
n
n
divides
2
n
2^n
2
n
,
n
−
1
n-1
n
−
1
divides
2
n
−
1
2^n - 1
2
n
−
1
, and
n
−
2
n-2
n
−
2
divides
2
n
−
2
2^n - 2
2
n
−
2
.
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