MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2002 India National Olympiad
2
2
Part of
2002 India National Olympiad
Problems
(1)
The smallest positive value
Source: India National Olympiad 2002, Problem 2
10/10/2005
Find the smallest positive value taken by
a
3
+
b
3
+
c
3
ā
3
a
b
c
a^3 + b^3 + c^3 - 3abc
a
3
+
b
3
+
c
3
ā
3
ab
c
for positive integers
a
a
a
,
b
b
b
,
c
c
c
. Find all
a
a
a
,
b
b
b
,
c
c
c
which give the smallest value
number theory solved
number theory