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Flanders Math Olympiad
2022 Flanders Math Olympiad
4
4
Part of
2022 Flanders Math Olympiad
Problems
(1)
kP (k + 1) - (k + 1)P (k) = k^2 + k + 1 for all k \in {1, 2, 3, . . . , 21, 22|
Source: Flanders Math Olympiad 2022 p4
12/24/2022
Determine all real polynomials
P
P
P
of degree at most
22
22
22
for which
k
P
(
k
+
1
)
−
(
k
+
1
)
P
(
k
)
=
k
2
+
k
+
1
kP (k + 1) - (k + 1)P (k) = k^2 + k + 1
k
P
(
k
+
1
)
−
(
k
+
1
)
P
(
k
)
=
k
2
+
k
+
1
for all
k
∈
{
1
,
2
,
3
,
.
.
.
,
21
,
22
}
k \in \{1, 2, 3, . . . , 21, 22\}
k
∈
{
1
,
2
,
3
,
...
,
21
,
22
}
.
algebra
polynomial