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Korea Junior Mathematics Olympiad
2022 Korea Junior Math Olympiad
4
4
Part of
2022 Korea Junior Math Olympiad
Problems
(1)
A strange distcrete functional equation seems analytic
Source: kjmo 2022 P4
10/29/2022
Find all function
f
:
N
⟶
N
f:\mathbb{N} \longrightarrow \mathbb{N}
f
:
N
⟶
N
such thatforall positive integers
x
x
x
and
y
y
y
,
f
(
x
+
y
)
−
f
(
x
)
f
(
y
)
\frac{f(x+y)-f(x)}{f(y)}
f
(
y
)
f
(
x
+
y
)
−
f
(
x
)
is again a positive integer not exceeding
202
2
2022
2022^{2022}
202
2
2022
.
algebra
functional equation
function