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2021-IMOC
N8
N8
Part of
2021-IMOC
Problems
(1)
Functional Equation using number of divisors of n
Source: IMOC 2021 N8
8/11/2021
Find all integer-valued polynomials
f
,
g
:
N
→
N
such that
∀
x
∈
N
,
τ
(
f
(
x
)
)
=
g
(
x
)
f, g : \mathbb{N} \rightarrow \mathbb{N} \text{ such that} \; \forall \; x \in \mathbb{N}, \tau (f(x)) = g(x)
f
,
g
:
N
→
N
such that
∀
x
∈
N
,
τ
(
f
(
x
))
=
g
(
x
)
holds for all positive integer
x
x
x
, where
τ
(
x
)
\tau (x)
τ
(
x
)
is the number of positive factors of
x
x
x
Proposed By - ckliao914
algebra
functional equation