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National and Regional Contests
Latvia Contests
Latvia BW TST
2021 Latvia Baltic Way TST
P16
P16
Part of
2021 Latvia Baltic Way TST
Problems
(1)
NT function with primes
Source: Latvia BW TST 2021 P16
9/26/2021
A function
f
:
N
→
N
f:\mathbb{N} \to \mathbb{N}
f
:
N
→
N
is given. If
a
,
b
a,b
a
,
b
are coprime, then
f
(
a
b
)
=
f
(
a
)
f
(
b
)
f(ab)=f(a)f(b)
f
(
ab
)
=
f
(
a
)
f
(
b
)
. Also, if
m
,
k
m,k
m
,
k
are primes (not necessarily different), then
f
(
m
+
k
−
3
)
=
f
(
m
)
+
f
(
k
)
−
f
(
3
)
.
f(m+k-3)=f(m)+f(k)-f(3).
f
(
m
+
k
−
3
)
=
f
(
m
)
+
f
(
k
)
−
f
(
3
)
.
Find all possible values of
f
(
11
)
f(11)
f
(
11
)
.
function
number theory