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Bulgarian Spring Mathematical Competition
2023 Bulgarian Spring Mathematical Competition
9.3
9.3
Part of
2023 Bulgarian Spring Mathematical Competition
Problems
(1)
Cute NT with binomials
Source: Bulgarian Spring Tournament 2023 9.3
3/25/2023
Given a prime
p
p
p
, find
gcd
(
(
2
p
p
1
)
,
(
2
p
p
3
)
,
…
,
(
2
p
p
2
p
p
−
1
)
)
\gcd(\binom{2^pp}{1},\binom{2^pp}{3},\ldots, \binom{2^pp}{2^pp-1})
g
cd
(
(
1
2
p
p
)
,
(
3
2
p
p
)
,
…
,
(
2
p
p
−
1
2
p
p
)
)
.
number theory