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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2005 All-Russian Olympiad Regional Round
9.7
9.7
Part of
2005 All-Russian Olympiad Regional Round
Problems
(1)
Arithmetic sequence with divisibility property
Source: All-Russian MO Round 4, 2005
4/2/2005
9.7 Is there an infinite arithmetic sequence
{
a
n
}
⊂
N
\{a_n\}\subset \mathbb N
{
a
n
}
⊂
N
s.t.
a
n
+
.
.
.
+
a
n
+
9
∣
a
n
.
.
.
a
n
+
9
a_n+...+a_{n+9}\mid a_n...a_{n+9}
a
n
+
...
+
a
n
+
9
∣
a
n
...
a
n
+
9
for all
n
n
n
? (V. Senderov)
arithmetic sequence
number theory proposed
number theory