MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2002 India National Olympiad
5
5
Part of
2002 India National Olympiad
Problems
(1)
An arithmetic progression
Source: India National Olympiad 2002, Problem 5
10/10/2005
Do there exist distinct positive integers
a
a
a
,
b
b
b
,
c
c
c
such that
a
a
a
,
b
b
b
,
c
c
c
,
−
a
+
b
+
c
-a+b+c
−
a
+
b
+
c
,
a
−
b
+
c
a-b+c
a
−
b
+
c
,
a
+
b
−
c
a+b-c
a
+
b
−
c
,
a
+
b
+
c
a+b+c
a
+
b
+
c
form an arithmetic progression (in some order).
arithmetic sequence
algebra unsolved
algebra