MathDB
Problems
Contests
National and Regional Contests
Serbia Contests
Serbia National Math Olympiad
2014 Serbia National Math Olympiad
4
4
Part of
2014 Serbia National Math Olympiad
Problems
(1)
SMO 2014
Source:
5/22/2015
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
number theory