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IMO LongList 1982 (AUS 3) - Values of f(1984), f(1985)
IMO LongList 1982 (AUS 3) - Values of f(1984), f(1985)
Source:
September 10, 2010
function
algebra proposed
algebra
Problem Statement
A function f has the following property: If
k
>
1
,
j
>
1
k > 1, j > 1
k
>
1
,
j
>
1
, and
gcd
(
k
,
j
)
=
m
\gcd(k, j) = m
g
cd
(
k
,
j
)
=
m
, then
f
(
k
j
)
=
f
(
m
)
(
f
(
k
m
)
+
f
(
j
m
)
)
f(kj) = f(m) (f\left(\frac km\right) + f\left(\frac jm\right))
f
(
kj
)
=
f
(
m
)
(
f
(
m
k
)
+
f
(
m
j
)
)
. What values can
f
(
1984
)
f(1984)
f
(
1984
)
and
f
(
1985
)
f(1985)
f
(
1985
)
take?
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