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National and Regional Contests
Iran Contests
Pre-Preparation Course Examination
2007 Pre-Preparation Course Examination
8
m is perfect square- Iran 3rd round-Number Theory 2007
m is perfect square- Iran 3rd round-Number Theory 2007
Source:
July 28, 2010
number theory unsolved
number theory
Problem Statement
Let
m
,
n
,
k
m,n,k
m
,
n
,
k
be positive integers and
1
+
m
+
n
3
=
(
2
+
3
)
2
k
+
1
1+m+n \sqrt 3=(2+ \sqrt 3)^{2k+1}
1
+
m
+
n
3
=
(
2
+
3
)
2
k
+
1
. Prove that
m
m
m
is a perfect square.
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