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Baltic Way
1993 Baltic Way
5
Factor, divisibility by 2^9
Factor, divisibility by 2^9
Source: Baltic Way 1993
June 15, 2012
number theory proposed
number theory
Problem Statement
Prove that for any odd positive integer
n
n
n
,
n
12
−
n
8
−
n
4
+
1
n^{12}-n^8-n^4+1
n
12
−
n
8
−
n
4
+
1
is divisible by
2
9
2^9
2
9
.
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