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Korea Winter Program Practice Test
2020 Korean MO winter camp
#3
#3
Part of
2020 Korean MO winter camp
Problems
(1)
Polynomials and primes
Source: 2020 Korean MO winter camp Test 1 P3
9/7/2020
Find all integer coefficient polynomials
Q
Q
Q
such that [*]
Q
(
n
)
≥
1
Q(n)\ge 1
Q
(
n
)
≥
1
∀
n
∈
Z
+
\forall n\in \mathbb{Z}_+
∀
n
∈
Z
+
. [*]
Q
(
m
n
)
Q(mn)
Q
(
mn
)
and
Q
(
m
)
Q
(
n
)
Q(m)Q(n)
Q
(
m
)
Q
(
n
)
have the same number of prime divisors
∀
m
,
n
∈
Z
+
\forall m,n\in\mathbb{Z}_+
∀
m
,
n
∈
Z
+
.
algebra
polynomial