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2013 China Western Mathematical Olympiad
8
8
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2013 China Western Mathematical Olympiad
Problems
(1)
2013 China Western Mathematical Olympiad ,Problem 8
Source: China Lanzhou 18 Aug 2013
8/18/2013
Find all positive integers
a
a
a
such that for any positive integer
n
≥
5
n\ge 5
n
≥
5
we have
2
n
−
n
2
∣
a
n
−
n
a
2^n-n^2\mid a^n-n^a
2
n
−
n
2
∣
a
n
−
n
a
.
induction
modular arithmetic
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number theory