MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Turkey EGMO TST
2018 Turkey EGMO TST
6
6
Part of
2018 Turkey EGMO TST
Problems
(1)
Turkey Egmo Tst 2018 p6
Source:
2/9/2018
Let
f
:
Z
+
→
Z
+
f:\mathbb{Z}_{+}\rightarrow\mathbb{Z}_{+}
f
:
Z
+
→
Z
+
is one to one and bijective function. Prove that
f
(
m
n
)
=
f
(
m
)
f
(
n
)
f(mn)=f (m)f (n)
f
(
mn
)
=
f
(
m
)
f
(
n
)
if and only if
l
c
m
(
f
(
m
)
,
f
(
n
)
)
=
f
(
l
c
m
(
m
,
n
)
)
lcm (f (m),f (n))=f(lcm(m,n))
l
c
m
(
f
(
m
)
,
f
(
n
))
=
f
(
l
c
m
(
m
,
n
))
number theory