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Indonesia National Science Olympiad 2010 - Day 1 Problem 1
Source:
9/28/2010
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be three different positive integers. Show that the sequence
a
+
b
+
c
,
a
b
+
b
c
+
c
a
,
3
a
b
c
a+b+c,ab+bc+ca,3abc
a
+
b
+
c
,
ab
+
b
c
+
c
a
,
3
ab
c
could be neither an arithmetic nor geometric progression.Fajar Yuliawan, Bandung
algebra unsolved
algebra