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Turkey Team Selection Test
2002 Turkey Team Selection Test
1
ab(a+b) | a^2+ab+b^2
ab(a+b) | a^2+ab+b^2
Source: Turkey TST 2002 - P1
April 6, 2013
number theory proposed
number theory
Problem Statement
If
a
b
(
a
+
b
)
ab(a+b)
ab
(
a
+
b
)
divides
a
2
+
a
b
+
b
2
a^2 + ab+ b^2
a
2
+
ab
+
b
2
for different integers
a
a
a
and
b
b
b
, prove that
∣
a
−
b
∣
>
a
b
3
.
|a-b|>\sqrt[3]{ab}.
∣
a
−
b
∣
>
3
ab
.
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