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Saint Petersburg Mathematical Olympiad
2018 Saint Petersburg Mathematical Olympiad
6
Division problem
Division problem
Source: St Petersburg Olympiad 2018, Grade 9, P6
July 13, 2018
number theory
Problem Statement
a
,
b
a,b
a
,
b
are odd numbers. Prove, that exists natural
k
k
k
that
b
k
−
a
2
b^k-a^2
b
k
−
a
2
or
a
k
−
b
2
a^k-b^2
a
k
−
b
2
is divided by
2
2018
2^{2018}
2
2018
.
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