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A,B,C have a common divisor greater than 1 - JBMO Shortlist
A,B,C have a common divisor greater than 1 - JBMO Shortlist
Source:
October 30, 2010
number theory proposed
number theory
Problem Statement
Find all pairs of integers
(
m
,
n
)
(m,n)
(
m
,
n
)
such that the numbers
A
=
n
2
+
2
m
n
+
3
m
2
+
2
A=n^2+2mn+3m^2+2
A
=
n
2
+
2
mn
+
3
m
2
+
2
,
B
=
2
n
2
+
3
m
n
+
m
2
+
2
B=2n^2+3mn+m^2+2
B
=
2
n
2
+
3
mn
+
m
2
+
2
,
C
=
3
n
2
+
m
n
+
2
m
2
+
1
C=3n^2+mn+2m^2+1
C
=
3
n
2
+
mn
+
2
m
2
+
1
have a common divisor greater than
1
1
1
.
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