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China Girls Math Olympiad
2016 China Girls Math Olympiad
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2016 China Girls Math Olympiad
Problems
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Chinese Girls Mathematical Olympiad 2016, Problem 3
Source: China Beijing ,12 Aug 2016
8/12/2016
Let
m
m
m
and
n
n
n
are relatively prime integers and
m
>
1
,
n
>
1
m>1,n>1
m
>
1
,
n
>
1
. Show that:There are positive integers
a
,
b
,
c
a,b,c
a
,
b
,
c
such that
m
a
=
1
+
n
b
c
m^a=1+n^bc
m
a
=
1
+
n
b
c
, and
n
n
n
and
c
c
c
are relatively prime.
number theory