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Serbia National Math Olympiad
2014 Serbia National Math Olympiad
4
SMO 2014
SMO 2014
Source:
May 22, 2015
number theory
Problem Statement
We call natural number
n
n
n
c
r
a
z
y
crazy
cr
a
zy
iff there exist natural numbers
a
a
a
,
b
>
1
b >1
b
>
1
such that
n
=
a
b
+
b
n=a^b+b
n
=
a
b
+
b
. Whether there exist
2014
2014
2014
consecutive natural numbers among which are
2012
2012
2012
c
r
a
z
y
crazy
cr
a
zy
numbers?Proposed by Milos Milosavljevic
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