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MathLinks Contest 5th
7.1
0571 number theory 5th edition Round 7 p1
0571 number theory 5th edition Round 7 p1
Source:
May 6, 2021
number theory
5th edition
Problem Statement
Prove that the numbers
(
2
n
−
1
i
)
,
i
=
0
,
1
,
.
.
.
,
2
n
−
1
−
1
,
{{2^n-1} \choose {i}}, i = 0, 1, . . ., 2^{n-1} - 1,
(
i
2
n
−
1
)
,
i
=
0
,
1
,
...
,
2
n
−
1
−
1
,
have pairwise different residues modulo
2
n
2^n
2
n
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