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1992 Iran MO (2nd round)
1
Prove that the number is divisible by 18 [Iran 1992]
Prove that the number is divisible by 18 [Iran 1992]
Source:
November 28, 2010
modular arithmetic
number theory proposed
number theory
Problem Statement
Prove that for any positive integer
t
,
t,
t
,
1
+
2
t
+
3
t
+
⋯
+
9
t
−
3
(
1
+
6
t
+
8
t
)
1+2^t+3^t+\cdots+9^t - 3(1 + 6^t +8^t )
1
+
2
t
+
3
t
+
⋯
+
9
t
−
3
(
1
+
6
t
+
8
t
)
is divisible by
18.
18.
18.
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