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Thailand Online MO
2022 Thailand Online MO
3
3
Part of
2022 Thailand Online MO
Problems
(1)
mn+1|f(m)f(n)+1
Source: 2022 Thailand Online MO P3
4/4/2022
Let
N
\mathbb{N}
N
be the set of positive integers. Across all function
f
:
N
→
N
f:\mathbb{N}\to\mathbb{N}
f
:
N
→
N
such that
m
n
+
1
divides
f
(
m
)
f
(
n
)
+
1
mn+1\text{ divides } f(m)f(n)+1
mn
+
1
divides
f
(
m
)
f
(
n
)
+
1
for all positive integers
m
m
m
and
n
n
n
, determine all possible values of
f
(
101
)
.
f(101).
f
(
101
)
.
function
functional equation
number theory