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2019 APMO
1
1
Part of
2019 APMO
Problems
(1)
Easy integer functional equation
Source: APMO 2019 P1
6/11/2019
Let
Z
+
\mathbb{Z}^+
Z
+
be the set of positive integers. Determine all functions
f
:
Z
+
ā
Z
+
f : \mathbb{Z}^+\to\mathbb{Z}^+
f
:
Z
+
ā
Z
+
such that
a
2
+
f
(
a
)
f
(
b
)
a^2+f(a)f(b)
a
2
+
f
(
a
)
f
(
b
)
is divisible by
f
(
a
)
+
b
f(a)+b
f
(
a
)
+
b
for all positive integers
a
,
b
a,b
a
,
b
.
function
number theory
algebra
functional equation
APMO