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Balkan MO
2016 Balkan MO
3
3
Part of
2016 Balkan MO
Problems
(1)
Primes Dividing Polynomial
Source: Balkan MO 2016, Problem 3
5/7/2016
Find all monic polynomials
f
f
f
with integer coefficients satisfying the following condition: there exists a positive integer
N
N
N
such that
p
p
p
divides
2
(
f
(
p
)
!
)
+
1
2(f(p)!)+1
2
(
f
(
p
)!)
+
1
for every prime
p
>
N
p>N
p
>
N
for which
f
(
p
)
f(p)
f
(
p
)
is a positive integer.Note: A monic polynomial has a leading coefficient equal to 1.(Greece - Panagiotis Lolas and Silouanos Brazitikos)
polynomial
number theory