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Serbia National Math Olympiad
2015 Serbia National Math Olympiad
2
2
Part of
2015 Serbia National Math Olympiad
Problems
(1)
Serbia national Olympiad Day 1 problem 2
Source: Serbia national Olympiad Day 1 problem 2
3/28/2015
Let
k
k
k
be fixed positive integer . Let
F
k
(
n
)
Fk(n)
F
k
(
n
)
be smallest positive integer bigger than
k
n
kn
kn
such that
F
k
(
n
)
ā
n
Fk(n)*n
F
k
(
n
)
ā
n
is a perfect square . Prove that if
F
k
(
n
)
=
F
k
(
m
)
Fk(n)=Fk(m)
F
k
(
n
)
=
F
k
(
m
)
than
m
=
n
m=n
m
=
n
.
number theory
TST