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Moldova Contests
Moldova Team Selection Test
2023 Moldova Team Selection Test
4
4
Part of
2023 Moldova Team Selection Test
Problems
(1)
P_n(X)=P_{n-1}(X)+3P_{n-1}(X)\cdot P_{n-2}(X)+P_{n-2}(X)
Source: Moldova TST 2023
4/7/2023
Polynomials
(
P
n
(
X
)
)
n
∈
N
(P_n(X))_{n\in\mathbb{N}}
(
P
n
(
X
)
)
n
∈
N
are defined as: P_0(X)=0, P_1(X)=X+2, P_n(X)=P_{n-1}(X)+3P_{n-1}(X)\cdot P_{n-2}(X)+P_{n-2}(X), (\forall) n\geq2. Show that if
k
k
k
divides
m
m
m
then
P
k
(
X
)
P_k(X)
P
k
(
X
)
divides
P
m
(
X
)
.
P_m(X).
P
m
(
X
)
.
algebra
polynomial