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IMO Shortlist
1968 IMO Shortlist
21
Find all positive integers k - ISL 1968
Find all positive integers k - ISL 1968
Source:
September 23, 2010
number theory
Divisibility
IMO Shortlist
Problem Statement
Let
a
0
,
a
1
,
…
,
a
k
(
k
≥
1
)
a_0, a_1, \ldots , a_k \ (k \geq 1)
a
0
,
a
1
,
…
,
a
k
(
k
≥
1
)
be positive integers. Find all positive integers
y
y
y
such that
a
0
∣
y
,
(
a
0
+
a
1
)
∣
(
y
+
a
1
)
,
…
,
(
a
0
+
a
n
)
∣
(
y
+
a
n
)
.
a_0 | y, (a_0 + a_1) | (y + a1), \ldots , (a_0 + a_n) | (y + a_n).
a
0
∣
y
,
(
a
0
+
a
1
)
∣
(
y
+
a
1
)
,
…
,
(
a
0
+
a
n
)
∣
(
y
+
a
n
)
.
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