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EGMO TST - Moldova
2021 Moldova EGMO TST
3
Prove that $9$ divides $A_n=16^n+4^n-2$ for every nonnegative integer $n$.
Prove that $9$ divides $A_n=16^n+4^n-2$ for every nonnegative integer $n$.
Source: Moldova EGMO TST 2021
February 4, 2023
number theory
Problem Statement
Prove that
9
9
9
divides
A
n
=
1
6
n
+
4
n
−
2
A_n=16^n+4^n-2
A
n
=
1
6
n
+
4
n
−
2
for every nonnegative integer
n
n
n
.
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