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Russia Contests
All-Russian Olympiad Regional Round
2000 All-Russian Olympiad Regional Round
9.2
9.2
Part of
2000 All-Russian Olympiad Regional Round
Problems
(1)
b|2a + 1, c|2b + 1, a|2c + 1 - All-Russian MO 2000 Regional (R4) 9.2
Source:
9/26/2024
Are there different mutually prime natural numbers
a
a
a
,
b
b
b
and
c
c
c
, greater than
1
1
1
, such that
2
a
+
1
2a + 1
2
a
+
1
is divisible by
b
b
b
,
2
b
+
1
2b + 1
2
b
+
1
is divisible by
c
c
c
and
2
c
+
1
2c + 1
2
c
+
1
is divisible by
a
a
a
?
number theory
divisible
divides