MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Saint Petersburg Mathematical Olympiad
2014 Saint Petersburg Mathematical Olympiad
1
Algebra with trinomial
Algebra with trinomial
Source: St Petersburg Olympiad 2014, Grade 10, P1
October 26, 2017
algebra
Problem Statement
f
(
x
)
f(x)
f
(
x
)
is square polynomial and
a
≠
b
a \neq b
a
=
b
such that
f
(
a
)
=
b
,
f
(
b
)
=
a
f(a)=b,f(b)=a
f
(
a
)
=
b
,
f
(
b
)
=
a
. Prove that there is not other pair
(
c
,
d
)
(c,d)
(
c
,
d
)
that
f
(
c
)
=
d
,
f
(
d
)
=
c
f(c)=d,f(d)=c
f
(
c
)
=
d
,
f
(
d
)
=
c
Back to Problems
View on AoPS