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2011 APMO
1
1
Part of
2011 APMO
Problems
(1)
Three numbers cannot be squares simultaneously
Source: APMO 2011
5/18/2011
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be positive integers. Prove that it is impossible to have all of the three numbers
a
2
+
b
+
c
,
b
2
+
c
+
a
,
c
2
+
a
+
b
a^2+b+c,b^2+c+a,c^2+a+b
a
2
+
b
+
c
,
b
2
+
c
+
a
,
c
2
+
a
+
b
to be perfect squares.
inequalities
quadratics
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number theory