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4
A 4
A 4
Source:
May 25, 2007
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algebra
polynomial
Vieta
symmetry
quadratics
Divisibility Theory
Problem Statement
If
a
,
b
,
c
a, b, c
a
,
b
,
c
are positive integers such that
0
<
a
2
+
b
2
−
a
b
c
≤
c
,
0 < a^{2}+b^{2}-abc \le c,
0
<
a
2
+
b
2
−
ab
c
≤
c
,
show that
a
2
+
b
2
−
a
b
c
a^{2}+b^{2}-abc
a
2
+
b
2
−
ab
c
is a perfect square.
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