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Iran Team Selection Test
2013 Iran Team Selection Test
8
8
Part of
2013 Iran Team Selection Test
Problems
(1)
Find all Arithmetic progressions
Source: Iran TST 2013:TST 2,Day 1,Problem 2
4/23/2013
Find all Arithmetic progressions
a
1
,
a
2
,
.
.
.
a_{1},a_{2},...
a
1
,
a
2
,
...
of natural numbers for which there exists natural number
N
>
1
N>1
N
>
1
such that for every
k
∈
N
k\in \mathbb{N}
k
∈
N
:
a
1
a
2
.
.
.
a
k
∣
a
N
+
1
a
N
+
2
.
.
.
a
N
+
k
a_{1}a_{2}...a_{k}\mid a_{N+1}a_{N+2}...a_{N+k}
a
1
a
2
...
a
k
∣
a
N
+
1
a
N
+
2
...
a
N
+
k
modular arithmetic
number theory
greatest common divisor
number theory proposed