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All-Russian Olympiad
2017 All-Russian Olympiad
7
7
Part of
2017 All-Russian Olympiad
Problems
(1)
Divisors of number
Source: All Russian Olympiad 2017,Day2,grade 11,P7
5/1/2017
There is number
N
N
N
on the board. Every minute Ivan makes next operation: takes any number
a
a
a
written on the board, erases it, then writes all divisors of
a
a
a
except
a
a
a
( Can be same numbers on the board). After some time on the board there are
N
2
N^2
N
2
numbers. For which
N
N
N
is it possible?
number theory
algebra