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2006 USAMO
4
4
Part of
2006 USAMO
Problems
(1)
USAMO sum equals product - original problems please
Source: USAMO 2006, Problem 4, proposed by Ricky Liu
4/20/2006
Find all positive integers
n
n
n
such that there are
k
≥
2
k \geq 2
k
≥
2
positive rational numbers
a
1
,
a
2
,
…
,
a
k
a_1, a_2, \ldots, a_k
a
1
,
a
2
,
…
,
a
k
satisfying
a
1
+
a
2
+
…
+
a
k
=
a
1
⋅
a
2
⋯
a
k
=
n
.
a_1 + a_2 + \ldots + a_k = a_1 \cdot a_2 \cdots a_k = n.
a
1
+
a
2
+
…
+
a
k
=
a
1
⋅
a
2
⋯
a
k
=
n
.
AMC
USA(J)MO
USAMO
quadratics
algebra unsolved
algebra