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Problems
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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2010 All-Russian Olympiad Regional Round
10.4
10.4
Part of
2010 All-Russian Olympiad Regional Round
Problems
(1)
a^5 is divisible by b^2, a^2 is divisible by b
Source: Russian Regional Olympiad 2010 10.4
8/24/2024
We call a natural number
b
b
b
lucky if for any natural number
a
a
a
such that
a
5
a^5
a
5
is divisible by
b
2
b^2
b
2
, the number
a
2
a^2
a
2
is divisible by
b
b
b
. Find the number of lucky natural numbers less than
2010
2010
2010
.
number theory
divisible