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Tiny divisibility FE with m^2 - n^2
Tiny divisibility FE with m^2 - n^2
Source: Own
July 15, 2023
algebra
functional equation
Divisibility
Problem Statement
Find all functions
f
:
N
→
N
f: \mathbb{N} \to \mathbb{N}
f
:
N
→
N
such that
m
+
f
(
n
)
∣
f
(
m
)
2
−
n
f
(
n
)
m+f(n) \mid f(m)^2 - nf(n)
m
+
f
(
n
)
∣
f
(
m
)
2
−
n
f
(
n
)
for all positive integers
m
m
m
and
n
n
n
. (Here,
f
(
m
)
2
f(m)^2
f
(
m
)
2
denotes
(
f
(
m
)
)
2
\left(f(m)\right)^2
(
f
(
m
)
)
2
.)
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