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Turkey Olympic Revenge
2023 Turkey Olympic Revenge
4
4
Part of
2023 Turkey Olympic Revenge
Problems
(1)
f(x)^2+2xf(y)+y^2 is a square
Source: Turkey Olympic Revenge 2023 P4
3/6/2023
Find all functions
f
:
Z
→
Z
f: \mathbb{Z}\to \mathbb{Z}
f
:
Z
→
Z
such that for all integers
x
x
x
and
y
y
y
, the number
f
(
x
)
2
+
2
x
f
(
y
)
+
y
2
f(x)^2+2xf(y)+y^2
f
(
x
)
2
+
2
x
f
(
y
)
+
y
2
is a perfect square.Proposed by Barış Koyuncu
functional equation
number theory
Revenge