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1999 Harvard-MIT Mathematics Tournament
3
1999 Oral #3: Distinct Positive Integers
1999 Oral #3: Distinct Positive Integers
Source:
October 20, 2012
Problem Statement
If
x
x
x
,
y
y
y
, and
z
z
z
are distinct positive integers such that
x
2
+
y
2
=
z
3
x^2+y^2=z^3
x
2
+
y
2
=
z
3
, what is the smallest possible value of
x
+
y
+
z
x+y+z
x
+
y
+
z
?
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