MathDB
Problems
Contests
National and Regional Contests
Iran Contests
Iran Team Selection Test
2009 Iran Team Selection Test
4
4
Part of
2009 Iran Team Selection Test
Problems
(1)
Iran TST 2009-Day2-P1
Source:
5/11/2009
Find all polynomials
f
f
f
with integer coefficient such that, for every prime
p
p
p
and natural numbers
u
u
u
and
v
v
v
with the condition:
p
∣
u
v
−
1
p \mid uv - 1
p
∣
uv
−
1
we always have
p
∣
f
(
u
)
f
(
v
)
−
1
p \mid f(u)f(v) - 1
p
∣
f
(
u
)
f
(
v
)
−
1
.
algebra
polynomial
number theory proposed
number theory