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Middle European Mathematical Olympiad
2017 Middle European Mathematical Olympiad
4
Minimum absolute difference of powers of 2 and 181
Minimum absolute difference of powers of 2 and 181
Source: MEMO 2017 I4
August 25, 2017
number theory
modular arithmetic
Problem Statement
Determine the smallest possible value of
∣
2
m
−
18
1
n
∣
,
|2^m - 181^n|,
∣
2
m
−
18
1
n
∣
,
where
m
m
m
and
n
n
n
are positive integers.
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