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Mathematics
Problem
Prove that for any geometric progression
{
a
n
}
\{a_n\}
{
a
n
}
and for all positive integers
p
>
q
p>q
p
>
q
, the relation
a
p
−
q
a
p
+
q
=
a
p
2
a_{p-q}\,a_{p+q}=a_p^2
a
p
−
q
a
p
+
q
=
a
p
2
holds.
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