MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad
1978 All Soviet Union Mathematical Olympiad
258
ASU 258 All Soviet Union MO 1978 f(x)=x^2-x+1, m, f(m), f(f(m)), ... rel.prime
ASU 258 All Soviet Union MO 1978 f(x)=x^2-x+1, m, f(m), f(f(m)), ... rel.prime
Source:
July 6, 2019
number theory
relatively prime
Problem Statement
Let
f
(
x
)
=
x
2
ā
x
+
1
f(x) = x^2 - x + 1
f
(
x
)
=
x
2
ā
x
+
1
. Prove that for every natural
m
>
1
m>1
m
>
1
the numbers
m
,
f
(
m
)
,
f
(
f
(
m
)
)
,
.
.
.
m, f(m), f(f(m)), ...
m
,
f
(
m
)
,
f
(
f
(
m
))
,
...
are relatively prime.
Back to Problems
View on AoPS