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National and Regional Contests
Turkey Contests
Turkey Olympic Revenge
2023 Turkey Olympic Revenge
3
3
Part of
2023 Turkey Olympic Revenge
Problems
(1)
Polynomial involving sum of digits
Source: Turkey Olympic Revenge 2023 P3
3/6/2023
Find all polynomials
P
P
P
with integer coefficients such that
s
(
x
)
=
s
(
y
)
⟹
s
(
∣
P
(
x
)
∣
)
=
s
(
∣
P
(
y
)
∣
)
.
s(x)=s(y) \implies s(|P(x)|)=s(|P(y)|).
s
(
x
)
=
s
(
y
)
⟹
s
(
∣
P
(
x
)
∣
)
=
s
(
∣
P
(
y
)
∣
)
.
for all
x
,
y
∈
N
x,y\in \mathbb{N}
x
,
y
∈
N
. Note:
s
(
x
)
s(x)
s
(
x
)
denotes the sum of digits of
x
x
x
.Proposed by Şevket Onur YILMAZ
number theory
olympic revenge
Polynomials
sum of digits