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Problems
Contests
National and Regional Contests
India Contests
Regional Mathematical Olympiad
2000 India Regional Mathematical Olympiad
6
6
Part of
2000 India Regional Mathematical Olympiad
Problems
(1)
Least positive integer
Source: Indian RMO 2000 Problem 6
10/27/2005
(i) Consider two positive integers
a
a
a
and
b
b
b
which are such that
a
a
b
b
a^a b^b
a
a
b
b
is divisible by
2000
2000
2000
. What is the least possible value of
a
b
ab
ab
? (ii) Consider two positive integers
a
a
a
and
b
b
b
which are such that
a
b
b
a
a^b b^a
a
b
b
a
is divisible by
2000
2000
2000
. What is the least possible value of
a
b
ab
ab
?