MathDB
Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2014 India PRMO
18
18
Part of
2014 India PRMO
Problems
(1)
2014 preRMO p18, f(mn) = f(m)f(n), f 1-1, N-> N, f (999) ?
Source:
8/9/2019
Let
f
f
f
be a one-to-one function from the set of natural numbers to itself such that
f
(
m
n
)
=
f
(
m
)
f
(
n
)
f(mn) = f(m)f(n)
f
(
mn
)
=
f
(
m
)
f
(
n
)
for all natural numbers
m
m
m
and
n
n
n
. What is the least possible value of
f
(
999
)
f (999)
f
(
999
)
?
function
algebra
minimum