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2012 Math Prize For Girls Problems
17
17
Part of
2012 Math Prize For Girls Problems
Problems
(1)
Math Prize 2012 Problem 17
Source:
9/24/2012
How many ordered triples
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
, where
a
a
a
,
b
b
b
, and
c
c
c
are from the set
{
1
,
2
,
3
,
…
,
17
}
\{ 1, 2, 3, \dots, 17 \}
{
1
,
2
,
3
,
…
,
17
}
, satisfy the equation
a
3
+
b
3
+
c
3
+
2
a
b
c
=
a
2
b
+
a
2
c
+
b
2
c
+
a
b
2
+
a
c
2
+
b
c
2
?
a^3 + b^3 + c^3 + 2abc = a^2b + a^2c + b^2c + ab^2 + ac^2 + bc^2 \, ?
a
3
+
b
3
+
c
3
+
2
ab
c
=
a
2
b
+
a
2
c
+
b
2
c
+
a
b
2
+
a
c
2
+
b
c
2
?
algebra
polynomial
symmetry