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1
Perfect square gives divisibility
Perfect square gives divisibility
Source: 2009 Greek TST,Pr.1
May 24, 2016
number theory
Problem Statement
Suppose that
a
a
a
is an even positive integer and
A
=
a
n
+
a
n
−
1
+
…
+
a
+
1
,
n
∈
N
∗
A=a^{n}+a^{n-1}+\ldots +a+1,n\in \mathbb{N^{*}}
A
=
a
n
+
a
n
−
1
+
…
+
a
+
1
,
n
∈
N
∗
is a perfect square.Prove that
8
∣
a
8\mid a
8
∣
a
.
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